Best Known (118, s)-Sequences in Base 16
(118, 255)-Sequence over F16 — Constructive and digital
Digital (118, 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
(118, 257)-Sequence in Base 16 — Constructive
(118, 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
(118, 512)-Sequence over F16 — Digital
Digital (118, 512)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 118 and N(F) ≥ 513, using
(118, 1815)-Sequence in Base 16 — Upper bound on s
There is no (118, 1816)-sequence in base 16, because
- net from sequence [i] would yield (118, m, 1817)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (118, 5447, 1817)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165447, 1817, S16, 3, 5329), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4721 222188 521491 430442 174240 331114 037874 207616 383361 176958 157800 106247 758921 795839 088957 986212 323289 346087 578186 316196 644399 280152 372748 836668 845360 610010 274803 046010 922342 592691 498569 939012 363665 983316 693101 163877 119076 429602 752078 924352 260518 755483 234487 145957 658053 982990 748483 894567 541006 693297 339304 488407 377200 057059 670904 046243 398049 854077 640199 962952 145537 820138 839450 824146 803408 281449 291357 898686 288108 452362 575632 780038 666058 594575 766739 064980 246162 306084 431947 087721 787169 825529 585382 347660 609832 395125 438203 996385 029515 159578 030345 202057 741908 775806 505168 422986 609305 086476 562798 928175 745514 666534 438434 996321 111157 864548 314535 919755 724313 716980 662722 273154 164826 604682 662179 357529 364954 406505 015050 257510 761240 602979 625712 895224 515249 183704 472296 048411 597106 387505 176948 092870 835251 808650 091382 209524 221511 463243 829096 449948 478157 841352 299451 671679 819594 279856 326609 997216 310466 229161 466242 967676 660692 431024 128814 695559 745340 244663 321396 079596 148597 730210 121513 942451 039741 907673 023556 547133 014011 628677 238184 504640 397548 943433 968226 924354 407048 773449 458481 947074 978151 681777 130359 030712 889243 607080 515412 433628 446528 685820 601574 142785 451492 017824 158705 768836 072486 439955 449493 953038 005929 993830 015716 887360 161926 957256 220754 231323 187254 210144 597756 401593 435610 929778 015071 638947 795653 775425 109371 152425 991145 053215 317621 262304 397916 519720 329192 228288 532766 849394 548875 564563 058286 292898 614124 283426 041688 599880 036790 666259 867380 449800 720347 720631 793166 567793 282005 178771 680508 727765 512150 160368 351710 655941 807262 941560 378787 725254 341479 610526 641775 063763 395831 403330 058001 674253 409669 605210 287178 294393 885322 845785 949192 766659 321677 406547 792129 689349 089543 980871 422215 880194 371583 237886 535187 845684 684159 336001 042403 812209 875955 456413 460665 039200 173317 016163 016680 786399 895460 202893 906168 283887 978061 832760 173163 162206 451270 671964 395783 117146 126481 666706 194409 273813 203079 535082 283254 138811 923596 023190 510745 490332 916669 544346 243129 110875 216597 995330 238452 711386 160661 362127 713095 488020 244999 759327 135466 110749 450263 628146 334172 287751 387688 672038 157871 258610 021317 940943 317284 364657 657745 967747 030722 375704 087088 675002 849503 827460 294299 870689 315203 468650 648579 464068 311834 805644 879172 932790 702435 610421 587524 684721 104387 202010 694949 582089 571693 965915 631131 102698 434142 862585 642179 401002 171563 291664 887792 382031 773530 643687 267025 913542 737629 896386 603677 680614 768339 927658 883307 144936 477196 871435 201191 902951 344100 084975 622137 098833 970836 819516 099406 878137 110712 458461 327788 823750 181353 189565 403911 620153 820741 418086 889228 470547 609242 322589 510647 817115 237372 574822 217607 344810 666353 566071 086411 166041 597626 239071 382607 075530 019280 723725 582141 191705 644438 767630 211743 266222 949301 292400 493481 469299 770974 210245 123235 652227 409174 928239 869101 924622 204526 938781 186924 385650 804188 665642 120472 665818 103453 993321 339979 386573 803923 621975 084852 082562 575125 508002 097466 597679 013165 641799 466902 009846 079399 469566 946262 098783 338113 877010 738495 542568 434871 889666 244620 230670 768727 052790 465414 037234 935078 795123 071564 716743 445990 498594 064787 263496 802992 368900 409196 635439 518122 867469 807396 968513 344825 426469 685663 788392 688028 365375 162276 432867 810074 482480 469700 282079 105636 496610 007025 495733 610219 072472 099841 927163 654172 852061 336132 184116 338607 595191 196498 458339 216115 415475 356869 904897 121848 315876 261261 976287 264270 289932 954143 544854 408915 782124 266847 659971 576598 588707 583362 481505 412991 366814 600143 727289 140325 508595 179183 554766 212081 715144 801678 166100 514117 262958 541749 524686 918371 261156 528543 177439 270320 746481 700563 792024 393284 808052 264633 942794 005180 192607 215185 586314 796324 137132 706361 840018 612124 315356 834884 961110 383550 419795 182798 412695 212368 738749 546057 347619 807274 699879 032659 375925 788929 430851 021355 770380 293336 929934 375288 105515 028549 955010 315939 581340 613435 340093 646549 697666 223459 900383 934367 515563 195035 336211 764353 542995 489717 327919 092340 293364 535491 459211 313226 321667 053080 031370 470689 085432 671059 750448 197144 047947 652321 216606 062928 262162 757772 848432 061880 491792 674239 698846 196185 260936 746126 334993 584524 786118 653182 548127 909567 891934 084135 621316 514589 145224 657988 718404 476451 775581 013651 078731 474736 235093 514042 131805 122604 860697 309651 414809 446865 614105 867758 651015 355514 722232 413615 357921 839024 910336 054079 869272 657781 348598 366024 640246 100133 996606 381136 303948 562216 068451 470106 239197 016386 779729 331801 330151 915786 849334 525580 360423 633263 703043 252043 996314 579545 726941 749364 458553 304252 606834 912946 909466 283065 096197 231246 610744 027779 775683 903279 257841 442815 918869 348945 576563 902166 125628 384096 335076 727639 974403 767150 670322 054882 672647 105721 520109 998678 073826 845495 309629 488379 640691 459648 585863 106053 446986 279676 673888 714794 464728 423919 255369 515833 930858 252496 386085 683248 452066 808733 815445 148059 144216 039455 488115 332440 472247 177102 330722 448319 286686 829254 604401 096101 036647 956556 548657 179586 846521 423470 039450 859457 062294 675143 143820 483717 566868 643462 048553 005572 163295 570477 912784 574778 039993 744729 154555 639313 922573 306563 353886 443179 737490 475193 466069 794670 164299 431467 369813 934709 028440 936711 869780 274450 965751 768958 687410 436381 228809 818003 132292 673954 335006 368277 445232 661414 141462 084750 719226 320996 469657 052159 758602 787337 525748 729762 713315 694793 412475 506073 601025 988053 885816 671011 809241 198416 393150 462520 393282 244644 759802 193719 170956 976037 122231 253364 160862 181693 689314 022249 952405 601582 665456 679230 121894 594039 165974 880610 449210 654832 194828 485731 248762 495458 626237 151494 897246 123594 590299 234709 771251 340778 688177 285027 323694 390152 500270 777269 508275 409950 406307 865307 163300 062437 257898 622501 974494 217219 133147 996850 373564 939225 322106 877271 318778 499706 941136 295353 004788 399183 129602 508196 649879 619711 091974 524749 234234 530339 451419 894031 200728 753703 068398 453636 756020 992633 774754 680864 848429 578070 433569 971170 471341 947880 870102 103751 124522 818954 061779 994265 164360 824968 655038 633549 800844 908672 734682 307221 490605 034585 900671 839232 342040 082306 544719 651431 369310 932265 065639 206329 546563 709019 777187 436287 849274 541640 288457 066936 315766 230877 582846 110832 309086 297627 032224 237787 849459 163566 201455 801907 502554 763333 905524 957604 031523 324823 778514 113801 714337 686797 838630 315264 135721 694863 385260 970030 711090 085524 607770 689829 848753 432797 016395 502163 361434 899816 928060 433839 432692 203473 447742 795935 001790 697498 783084 670343 953680 416272 245025 271768 692135 724016 016651 166506 185567 640128 341970 583281 202745 157602 235648 755568 302355 773435 101884 874749 891522 071853 027762 192129 403008 774799 253731 787725 457860 464548 700312 850420 567871 234650 392155 662256 345337 252372 124954 040344 857369 518251 500953 136897 888009 321201 354794 474636 597945 833518 467280 684533 678080 / 533 > 165447 [i]
- extracting embedded OOA [i] would yield OOA(165447, 1817, S16, 3, 5329), but
- m-reduction [i] would yield (118, 5447, 1817)-net in base 16, but