Best Known (115, s)-Sequences in Base 16
(115, 255)-Sequence over F16 — Constructive and digital
Digital (115, 255)-sequence over F16, using
- t-expansion [i] based on digital (75, 255)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
(115, 257)-Sequence in Base 16 — Constructive
(115, 257)-sequence in base 16, using
- t-expansion [i] based on (113, 257)-sequence in base 16, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
(115, 339)-Sequence over F16 — Digital
Digital (115, 339)-sequence over F16, using
- t-expansion [i] based on digital (101, 339)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 101 and N(F) ≥ 340, using
(115, 1770)-Sequence in Base 16 — Upper bound on s
There is no (115, 1771)-sequence in base 16, because
- net from sequence [i] would yield (115, m, 1772)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (115, 5312, 1772)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165312, 1772, S16, 3, 5197), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6605 133872 203045 412701 515745 882236 803919 442818 075816 795053 734104 452557 706710 799979 497058 426491 571185 302901 670100 170860 042166 130481 097305 503694 875182 519265 569012 392125 177540 044803 488899 605398 412885 718313 967651 707869 935312 825777 653112 447644 742719 267609 329465 546898 502509 077810 480448 637572 970924 648808 664062 140808 372906 572630 232159 087391 498348 087155 586774 394606 164239 914468 879140 391078 715689 626102 987984 457196 739913 322790 474825 036799 264056 455716 281597 784340 010416 578245 190398 174527 346007 023947 942407 962058 779468 204806 289941 492506 055223 096864 225354 248795 684648 585633 905726 613393 142373 975985 761604 953356 831401 402644 455297 871108 737520 242079 019147 304904 896580 005329 963951 877217 922772 078250 100716 953852 514005 652384 900888 018239 287362 148501 971870 715119 926966 359363 358161 950836 796714 275468 456180 595870 276134 272852 070792 219539 784932 206875 289920 212383 080460 616206 902370 750698 271667 975791 058175 273255 508864 152780 940662 114050 088514 250252 237827 882865 180223 659334 968639 128992 072054 919307 407979 955021 418824 802931 071849 100848 275633 220603 387094 876791 750270 465271 905340 459460 567546 411592 309634 350806 485437 924113 437299 101360 493200 535096 693716 644843 652421 807341 557795 308555 679854 338846 391424 579815 385599 192923 240875 933979 306450 585977 948375 040217 504483 705221 101639 470584 441970 032137 858345 753737 379214 663351 482218 477637 219152 454907 781167 003905 893147 609094 032198 775117 074447 847470 337375 753472 696895 844326 480510 597019 477690 197903 093536 507161 786550 035449 982888 011837 013914 630431 820781 107902 231517 581330 362006 256449 482593 570163 981668 837676 336805 662310 660379 636631 428733 779236 471184 880153 058249 555446 454730 293423 188466 150651 817624 215395 272299 950470 097202 129891 101620 623068 688348 740419 662893 210168 437114 453276 892933 827990 010328 977195 006986 547943 424636 842336 716654 020922 699810 741827 012928 592714 266913 352851 780406 908630 113951 947793 065335 736809 766425 610020 863967 882774 294364 455270 180882 893894 498224 984719 453489 896252 708235 472625 988036 992390 928822 890362 363626 141538 136778 977703 603755 031600 630020 154695 177805 295341 777616 940866 676826 438659 222876 583253 492388 507032 138231 510458 620677 216494 643048 258212 846076 488565 352822 614342 701511 553344 529587 324623 350562 373037 276409 266595 302906 585677 141938 908751 413703 565591 177808 964373 790500 291345 233369 054643 285772 138075 077764 884655 143810 715199 036239 109637 866680 022879 324487 403764 943936 465265 116071 174253 809350 248587 742589 796190 953148 989536 315027 111431 348722 399259 889989 443163 816121 958340 540950 469283 701097 529048 438802 292638 366857 468716 928714 292722 998416 281519 823987 131707 617877 044949 048128 522461 202361 155439 706709 603702 651077 140871 865307 109899 910317 095402 305599 584061 703775 378803 820017 292169 715590 201754 251480 580838 573295 262042 247139 067119 759889 138690 402095 871711 568251 033909 228457 678511 794596 830233 281790 170919 638697 244493 231597 321345 637687 401705 456487 142872 301059 466924 977964 362149 197031 954652 385545 621145 734158 889452 708095 582453 873761 958182 579323 118798 087954 330350 614940 096989 037773 257545 048345 740344 062790 549958 465542 982817 107508 184400 773592 535962 829440 356576 336496 111379 735588 600766 507084 715710 807645 369248 611201 489447 256373 252559 022311 139212 266765 581419 379619 939661 906722 498591 297394 040531 233180 957215 007656 554238 931136 993500 667477 663714 517598 756102 617291 388788 747633 617018 042785 516547 625766 398667 781425 337361 988982 310061 347029 605444 645688 284175 707383 265476 320130 591975 006293 588049 810089 056594 143558 901117 530854 516788 506344 569861 503415 681659 630946 016690 988901 937052 232710 578107 193834 446368 640582 830190 589253 665109 984591 297878 298269 760912 565690 093818 215900 687598 670320 379893 319471 903442 932955 605247 870330 668442 340942 323689 800304 217211 065575 825373 579694 112553 143783 347770 520151 701840 789509 485894 015149 181882 092918 548145 692973 714068 060363 172414 360696 169371 844659 559685 136291 556950 759849 717664 913817 145110 988795 718161 674578 496217 301081 381956 852705 777114 242648 151713 523825 403107 525912 414909 266802 505824 948417 777876 547657 828322 549218 984061 935214 935831 743882 632306 720866 342299 865581 894025 518358 096882 969938 768816 413845 001265 658988 806063 132289 680472 779045 417956 552629 789036 782454 173802 836643 557322 188623 954256 205405 955004 098012 989092 675920 949472 054394 720526 110291 346492 643961 977265 055253 666790 588846 985489 187393 918590 862142 033366 204993 254481 386031 121504 226512 620255 034454 975195 191279 873599 417845 108450 730113 946542 594149 608190 709978 789955 828798 980471 674220 766452 428592 083556 693864 328663 945614 016648 978712 582981 530824 947867 276780 245129 125695 068529 786543 873291 648868 842946 338608 051963 222572 677371 088976 825357 260101 700054 908906 161861 210527 474088 812246 181152 474599 392230 942825 164601 600004 256265 097133 463265 200686 403138 343376 873724 539898 038591 669691 209966 326778 487749 452301 032829 653427 282089 133523 713451 783983 701406 468719 909284 316538 456804 955122 116742 168340 260143 738304 229852 440699 123972 563929 092966 092715 733112 772207 798427 745914 837927 929653 359937 368936 142517 467931 969777 226239 055333 333690 194020 867352 997827 695022 026553 488078 952858 229401 225910 327134 547817 097620 227798 760083 628515 552338 876270 049318 878993 478425 169686 001315 307421 733746 594230 713381 543694 662655 642995 499191 026536 488450 677183 841233 389175 680915 932464 438437 547226 697742 618884 081029 126527 362862 951247 607396 218310 099201 788401 602759 870018 373967 937457 378099 030412 960545 178952 181824 156788 783503 793702 226112 142274 971621 066068 468621 477944 669630 413015 389295 523367 114302 852682 440136 569241 260140 305203 859344 724448 954003 008040 853770 130459 175365 801795 464799 889057 296406 214991 284786 585842 169648 123460 303577 541118 552988 428682 703671 509049 024891 004388 417174 638166 204197 182026 825347 592036 521561 323715 999696 771118 339218 411814 311883 336638 707384 022650 290285 008633 488715 260314 660524 464852 397797 347589 432221 680685 043265 113889 558965 691191 425041 468973 373281 013097 336870 730665 262299 630682 620383 670292 638671 535938 565758 645446 270529 798121 627301 068558 995590 563828 438734 567094 454554 647275 458195 449922 523943 706271 914691 435460 651473 054462 439325 722867 224911 096527 636940 863335 402358 109512 470599 532494 153601 246266 793292 312369 743201 845658 726481 848077 200511 812944 283202 338157 538515 918862 456650 198796 394171 732243 431774 260311 919093 654052 968359 960589 407174 384834 421209 189861 717127 998383 019437 072781 773106 892580 282352 793635 267280 874003 971274 307710 604335 282172 750756 995264 798991 580470 976545 957392 717781 233571 403758 991740 448137 316272 616865 339142 922730 075824 117209 102339 291279 625091 462978 073386 719002 178984 594662 772356 744261 491986 707107 153600 131573 831792 746525 401819 402158 937761 479114 330432 517146 182114 239773 536031 878456 797159 299910 463916 143275 993886 783208 917412 058780 826823 684824 067571 974144 / 2599 > 165312 [i]
- extracting embedded OOA [i] would yield OOA(165312, 1772, S16, 3, 5197), but
- m-reduction [i] would yield (115, 5312, 1772)-net in base 16, but