Best Known (28, 28+∞, s)-Nets in Base 7
(28, 28+∞, 32)-Net over F7 — Constructive and digital
Digital (28, m, 32)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 31)-sequence over F7, using
- t-expansion [i] based on digital (27, 31)-sequence over F7, using
(28, 28+∞, 78)-Net over F7 — Digital
Digital (28, m, 78)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 77)-sequence over F7, using
- t-expansion [i] based on digital (27, 77)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 27 and N(F) ≥ 78, using
- t-expansion [i] based on digital (27, 77)-sequence over F7, using
(28, 28+∞, 187)-Net in Base 7 — Upper bound on s
There is no (28, m, 188)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (28, 560, 188)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7560, 188, S7, 3, 532), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 104 490916 966852 858721 387317 612469 555264 720689 327601 266028 296941 599894 128156 110267 241684 048013 445967 928304 177565 180787 969970 210037 976826 157779 536135 917937 753079 761805 473404 869301 760485 988736 621288 052538 033166 640249 672734 909938 294341 904054 802036 561849 919687 688362 480215 694854 390199 922537 326065 025580 446830 922204 875369 795633 217252 816514 591920 807980 235930 271172 018698 933815 494365 290228 343015 581615 073619 478455 520343 249682 061203 236178 882629 329552 764124 240745 270617 820069 405744 016581 / 533 > 7560 [i]
- extracting embedded OOA [i] would yield OOA(7560, 188, S7, 3, 532), but