Best Known (18, 18+57, s)-Nets in Base 7
(18, 18+57, 26)-Net over F7 — Constructive and digital
Digital (18, 75, 26)-net over F7, using
- net from sequence [i] based on digital (18, 25)-sequence over F7, using
(18, 18+57, 51)-Net over F7 — Digital
Digital (18, 75, 51)-net over F7, using
- net from sequence [i] based on digital (18, 50)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 18 and N(F) ≥ 51, using
(18, 18+57, 299)-Net in Base 7 — Upper bound on s
There is no (18, 75, 300)-net in base 7, because
- 3 times m-reduction [i] would yield (18, 72, 300)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(772, 300, S7, 54), but
- the linear programming bound shows that M ≥ 489103 554816 394657 800399 037864 659820 501497 415398 742685 371165 942106 365907 984558 305747 707707 237646 393998 681516 262241 865730 620908 433038 750000 / 65991 622295 854220 768278 534644 534429 740960 702156 273507 041087 721301 002664 801349 > 772 [i]
- extracting embedded orthogonal array [i] would yield OA(772, 300, S7, 54), but