Best Known (64−47, 64, s)-Nets in Base 27
(64−47, 64, 96)-Net over F27 — Constructive and digital
Digital (17, 64, 96)-net over F27, using
- t-expansion [i] based on digital (11, 64, 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
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(64−47, 64, 100)-Net in Base 27 — Constructive
(17, 64, 100)-net in base 27, using
- base change [i] based on digital (1, 48, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(64−47, 64, 144)-Net over F27 — Digital
Digital (17, 64, 144)-net over F27, using
- t-expansion [i] based on digital (16, 64, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
(64−47, 64, 3009)-Net in Base 27 — Upper bound on s
There is no (17, 64, 3010)-net in base 27, because
- 1 times m-reduction [i] would yield (17, 63, 3010)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 507469 972878 010420 593906 148779 789098 959950 587244 626364 951487 552443 644161 413424 055147 711993 > 2763 [i]