Best Known (109, s)-Sequences in Base 27
(109, 323)-Sequence over F27 — Constructive and digital
Digital (109, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
(109, 324)-Sequence over F27 — Digital
Digital (109, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
(109, 2896)-Sequence in Base 27 — Upper bound on s
There is no (109, 2897)-sequence in base 27, because
- net from sequence [i] would yield (109, m, 2898)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (109, 5793, 2898)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275793, 2898, S27, 2, 5684), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 314 587017 648871 182973 915585 823968 969226 761980 483481 731854 962313 361224 923396 146321 279006 584702 664254 751181 461853 474541 690623 944595 400215 446228 006348 156896 274868 149135 051738 103358 977481 094659 410427 513368 110378 586651 869420 219033 239267 663137 580344 302421 110160 507421 277431 573864 653534 056271 417144 040045 315009 357272 911430 937078 745073 012160 105380 360671 938955 021744 446151 452254 763659 512211 301460 285281 145679 980938 261983 682624 226505 282441 430798 771386 483947 363122 651643 846053 765156 215531 963319 647550 709040 358951 920711 812558 625939 568848 425128 985927 320436 702500 180111 821498 900750 783823 847033 275325 369481 839022 169062 225977 246811 297007 670814 287297 345706 184831 864076 213401 802217 407421 335263 265912 168353 138951 928315 023086 228092 501260 364487 188384 686899 530195 186615 576132 132431 710796 474876 077565 572994 764883 100157 273397 884926 959135 030486 327390 148516 649446 394024 510343 570078 211748 785990 861372 637731 801011 465947 002456 252546 953503 111904 152472 574813 277974 987381 058484 722353 622810 043236 569748 554200 843621 515221 500592 891956 866144 329211 244131 343489 232800 332040 369304 693100 687749 162523 016240 064131 428224 528789 395229 320688 311640 668651 856037 458488 720105 997867 662310 469622 845091 840382 239536 790044 662564 473297 125154 900980 318998 570906 600500 438417 773021 904604 067355 450699 142233 078438 548715 976318 691935 237950 401900 731527 414093 079137 686373 976352 334315 184710 777562 160094 300193 340099 131824 502661 363419 929121 616724 025364 550958 528854 400742 080997 195613 365869 722775 422852 457912 605390 284464 531365 117154 773686 622674 912667 536315 008100 009507 059266 630259 432242 932781 885129 036820 238582 887596 062628 295193 898431 985869 728031 544968 190824 966102 749165 578852 859328 958774 205586 739411 217447 675180 196808 407103 503405 209012 618745 342245 249297 722724 026646 148941 739711 514322 984932 755762 156593 594709 973556 970574 349994 708333 373664 395225 842403 739809 855822 860907 860310 237948 253068 929649 019042 120256 734376 657369 784250 671514 766472 355480 319910 067074 834016 602364 124753 156992 018824 093069 062534 849889 471245 424238 355116 852108 137945 169340 607272 965732 452379 170070 535645 889638 640754 188814 418720 506716 367471 400666 028599 939005 453084 600050 426672 483500 915258 895704 974458 217116 268682 839084 100553 281520 289260 934969 949806 295814 924875 496659 545308 107068 025514 608598 178157 830270 180858 565489 026659 475290 332252 876499 698488 730247 746592 107400 880921 995874 563587 149814 711332 190048 304296 268065 039291 088537 317694 464463 478200 823676 391630 000330 407983 031109 474643 825379 855278 567053 849151 896782 874543 503459 068203 030977 009683 825876 389934 967825 783764 657934 647632 993724 928234 239283 446145 887561 154709 082292 937310 595568 781374 878673 548221 822480 576592 007955 836303 041832 366916 087965 794868 134809 022894 964470 557868 025664 146396 345261 230701 102695 489800 814939 341704 794704 327560 985896 247654 026014 956433 708653 449580 275785 976528 213057 675711 766452 762810 976985 887975 956861 809057 636477 033347 132575 922261 522621 892722 067933 685092 289034 666337 581288 369232 324692 582383 937938 698095 870186 771060 988367 580104 784508 807266 112349 736196 722536 932136 172917 018996 955548 491966 986138 075457 711325 175313 965465 285450 346862 397417 747203 394871 391186 787633 339251 734926 628878 000642 129359 125407 422958 435447 447969 303273 235864 791104 846551 448062 323778 395573 561933 404484 905134 622720 116720 827919 723035 425162 799303 391742 838765 149603 968212 704362 469040 376953 685103 303499 180456 531130 528510 496239 576287 262316 176499 879139 980954 536085 638599 886453 940325 632827 512879 746423 965153 203490 122629 404737 494917 618930 190451 037379 583795 763775 703288 368134 452257 314484 766428 169773 885708 546482 948646 792039 900930 581803 119157 009105 185814 447609 767221 735210 671100 914833 559745 056223 832471 927373 272752 871031 858645 786559 467923 238347 772521 905006 197588 668875 686468 434143 021668 179591 347046 835473 822405 617058 286908 308355 707499 900972 390817 135478 975094 779917 478112 861131 513858 291504 808356 236041 836022 683110 190017 493820 678835 476579 729878 527235 358189 522580 230549 788521 215665 541541 737522 805546 984147 455324 794906 985427 120686 426570 775905 260802 812717 045750 296403 014951 986284 522258 652413 317864 053564 038624 020172 465359 010328 263128 416870 588855 277661 353817 632311 761746 806340 908669 311016 855229 272440 966337 828075 803985 055323 933638 916443 623850 764743 564372 863702 750683 710517 537065 714482 084249 695461 933522 768194 352115 982622 697484 633863 348564 079240 263909 841415 346769 697096 209612 936517 929095 616325 321110 787465 373723 349549 075429 277866 334918 052108 614310 125080 424978 431891 882941 830503 417257 362846 366361 650576 071869 780390 916515 452608 749426 617469 167351 985328 263127 863831 193322 956089 354145 630823 844207 709947 309394 638910 210584 001199 306636 796634 935382 823286 938957 692200 242432 607719 108029 279208 527794 687224 615041 404395 103810 467232 014858 053664 967027 045293 393684 673583 173490 705328 340446 876055 072775 079450 775181 634387 747554 513906 237023 152018 901284 999610 431202 039452 834166 954796 974805 440713 556127 342042 344433 948200 412800 212922 506771 038189 322544 792138 402521 715481 349976 180567 353233 086501 342749 719007 682484 720442 281858 142258 474186 987989 584676 790848 074723 618605 108376 264640 592295 655741 450438 880635 531172 768545 609891 051219 561940 280947 522696 812036 217521 088864 183487 778709 077563 204234 502787 002259 086454 875305 173273 422630 875903 419871 127572 905720 392483 609894 160542 950904 854403 249356 179859 556971 052339 372605 623184 264885 470235 747372 912355 748287 033118 832027 774913 409644 482194 214204 937015 577224 310461 806943 275870 517785 086537 140511 662447 500672 782059 816816 036999 355244 845901 709707 634032 539563 685893 210643 586572 552350 741286 359583 985391 444529 199847 081780 600749 466195 323895 701165 356552 730943 029854 689051 962537 810962 035894 716321 828734 491954 167647 254346 643728 582116 450239 608268 238563 614811 499750 572687 202509 128480 158928 680295 615797 579665 140160 324037 684831 847356 991315 208959 408020 485290 925492 552791 503036 147447 743766 518093 971293 286919 965964 146443 727927 645286 917922 380672 184832 758343 474896 203723 676758 639714 021096 238837 784714 060533 623958 789318 285722 403057 561405 401818 225925 402905 418732 704617 797988 078510 971551 277119 162218 622680 451212 262636 054578 591402 694110 433820 830559 830643 806814 448637 970269 380377 183558 619002 296203 081556 113755 373182 468651 129914 198198 214287 561354 186965 210911 745365 382237 101170 272339 882752 888009 093153 740895 062550 959998 129358 665414 104264 971365 955539 007742 259030 850677 103409 946764 620563 019919 525313 607337 869606 711433 569358 095765 162693 765087 269029 881266 695569 370798 218916 484491 632931 598754 164836 270337 308133 222871 275023 726869 315331 474351 526160 413087 368592 077450 895839 532544 815877 969932 676068 131232 867045 363224 720981 106384 070066 212655 136384 278393 450869 822334 454543 540925 884475 548524 609035 135135 806728 594180 828013 573446 946022 917311 545370 854501 812227 689910 101609 949839 260820 920272 937312 094867 324028 531043 181905 529744 520213 341375 918606 567708 418186 454523 565398 013821 372070 927873 349589 442174 047905 709685 437535 475868 364519 001809 769876 696679 692069 946169 908112 642897 006709 348018 589240 685802 304558 552613 103294 388058 157549 111072 167499 377516 080454 595474 722645 961148 253601 607653 634705 041739 823976 910758 760210 912657 758093 519548 947590 373972 990709 933367 495471 637180 763572 841905 133578 269070 844755 911109 713913 109978 345277 195937 500878 137599 427779 365332 651207 042735 907199 306677 005907 832567 991352 020943 587730 124480 201495 130360 118673 669769 688379 665844 220042 531802 317592 725615 331107 964337 847850 531135 336944 383388 601997 552855 547355 131740 760816 347096 659878 245740 087202 273340 499546 385227 522086 459234 624624 811014 871666 903357 284276 938206 718539 888220 531741 097558 251515 102977 277836 559472 707985 010421 386604 455241 696576 201809 578563 029691 475592 844644 989415 639378 409294 943244 860336 877931 023444 647996 603323 326463 693490 019834 135788 292402 788928 618073 943401 508751 491576 594124 455506 131375 322067 286731 453086 907670 305617 624789 258853 147667 006241 240790 594393 090347 419122 814221 161991 856041 017945 740419 166521 277266 853501 430040 289930 723390 438648 344902 286383 149145 821609 072758 257361 721244 736464 622324 138799 642393 875502 106099 022978 075804 805048 350183 028476 482234 620611 072008 184328 976827 668114 226358 039169 869307 664013 461799 588900 573088 041651 658208 217790 922766 742155 650528 329535 186939 181036 648701 633554 221550 612004 138606 753492 124710 141502 416186 217959 713796 242380 695595 506979 742662 694979 485559 856663 623924 936012 234071 360235 129459 681526 063148 318846 691855 581510 749604 781365 864725 689963 127960 234503 517994 569828 012916 836671 119976 148537 185767 166099 911732 381355 104647 983063 987019 536294 749095 049490 837286 399767 945338 939230 807440 331828 934448 177711 684424 064786 214242 923771 864478 031764 130110 592107 786032 683897 620215 478512 609242 233723 326429 065987 130297 337723 114435 543297 486135 / 379 > 275793 [i]
- extracting embedded OOA [i] would yield OOA(275793, 2898, S27, 2, 5684), but
- m-reduction [i] would yield (109, 5793, 2898)-net in base 27, but