Best Known (49−29, 49, s)-Nets in Base 7
(49−29, 49, 28)-Net over F7 — Constructive and digital
Digital (20, 49, 28)-net over F7, using
- net from sequence [i] based on digital (20, 27)-sequence over F7, using
(49−29, 49, 54)-Net over F7 — Digital
Digital (20, 49, 54)-net over F7, using
- t-expansion [i] based on digital (19, 49, 54)-net over F7, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 19 and N(F) ≥ 54, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
(49−29, 49, 786)-Net in Base 7 — Upper bound on s
There is no (20, 49, 787)-net in base 7, because
- 1 times m-reduction [i] would yield (20, 48, 787)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 36725 875606 450878 479352 078857 932123 206229 > 748 [i]