Best Known (56−43, 56, s)-Nets in Base 7
(56−43, 56, 21)-Net over F7 — Constructive and digital
Digital (13, 56, 21)-net over F7, using
- net from sequence [i] based on digital (13, 20)-sequence over F7, using
(56−43, 56, 48)-Net over F7 — Digital
Digital (13, 56, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(56−43, 56, 214)-Net in Base 7 — Upper bound on s
There is no (13, 56, 215)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(756, 215, S7, 43), but
- the linear programming bound shows that M ≥ 1 488962 621741 545770 397339 272823 291858 863490 708411 604681 016011 605620 094901 524255 111902 744285 820291 037617 250034 / 6 730967 821572 051534 745282 607389 451158 475810 799606 199909 525993 > 756 [i]