Best Known (58−47, 58, s)-Nets in Base 27
(58−47, 58, 96)-Net over F27 — Constructive and digital
Digital (11, 58, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(58−47, 58, 100)-Net over F27 — Digital
Digital (11, 58, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(58−47, 58, 1266)-Net in Base 27 — Upper bound on s
There is no (11, 58, 1267)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 57, 1267)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3879 879188 738513 689972 283889 945893 130659 154299 789315 022018 775960 174833 383059 744155 > 2757 [i]