Best Known (106, s)-Sequences in Base 7
(106, 86)-Sequence over F7 — Constructive and digital
Digital (106, 86)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 87 from GarcÃa–Stichtenoth tower as constant field extension [i]
(106, 104)-Sequence over F7 — Digital
Digital (106, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
(106, 659)-Sequence in Base 7 — Upper bound on s
There is no (106, 660)-sequence in base 7, because
- net from sequence [i] would yield (106, m, 661)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (106, 1979, 661)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71979, 661, S7, 3, 1873), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 542185 901223 033309 828702 558905 789911 647040 827410 751123 304195 041380 980407 875921 426724 689677 396179 448997 078396 834576 064165 179811 349023 415633 807459 252892 674708 867294 185064 738696 608461 347782 354563 580635 631278 122846 788272 315773 825072 306316 149252 414040 178872 178689 165077 050406 781684 470585 018740 414520 277000 596942 803486 202218 465865 277637 491941 590966 485179 836063 441236 281101 732281 232272 506234 142994 679271 606227 713533 753795 136654 145568 241900 297203 350509 827235 445407 013017 190067 248441 913733 309645 068957 591412 748246 950890 463420 904457 186839 678979 123296 852586 028691 867231 780054 746119 851222 414383 573121 100461 516102 549822 322303 149571 454302 005930 616447 418494 472638 756266 715804 900375 009886 123463 936950 095224 331731 792050 709309 967569 306514 108193 422560 426644 259924 897689 918890 884328 706732 906302 326919 695074 911061 715347 121782 386574 510684 243962 980191 720423 239963 487677 395893 205013 327263 251215 662790 077249 115467 787927 854350 165506 267434 712151 247004 218572 161403 626711 217313 888527 620135 181565 862988 344496 716192 452634 043508 380229 988243 765960 749978 874244 626250 483537 427254 643664 231895 658667 788316 944625 794099 416121 883428 436542 472237 404383 725698 437412 635561 281545 766715 454542 235192 671112 260174 705576 446402 218865 615629 659030 386291 336961 273629 283511 175767 667885 335285 548395 571139 323999 252003 690662 487274 268726 206264 025124 220495 578812 925829 663821 755316 306800 516266 899494 663371 884215 337893 317108 460277 546252 755407 586481 205168 747503 742077 422711 043319 799606 787795 103493 963230 985995 691000 731801 229663 065659 765240 195584 436949 778439 307667 890902 327966 989715 314997 926396 469941 974294 846702 648208 489831 852554 588354 262032 588008 627207 422844 872219 945867 963766 819977 239143 665672 171490 972439 545981 215548 192789 079100 260145 / 937 > 71979 [i]
- extracting embedded OOA [i] would yield OOA(71979, 661, S7, 3, 1873), but
- m-reduction [i] would yield (106, 1979, 661)-net in base 7, but