Best Known (33−27, 33, s)-Nets in Base 64
(33−27, 33, 128)-Net over F64 — Constructive and digital
Digital (6, 33, 128)-net over F64, using
- t-expansion [i] based on digital (5, 33, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(33−27, 33, 150)-Net in Base 64 — Constructive
(6, 33, 150)-net in base 64, using
- 2 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
(33−27, 33, 161)-Net over F64 — Digital
Digital (6, 33, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
(33−27, 33, 2505)-Net in Base 64 — Upper bound on s
There is no (6, 33, 2506)-net in base 64, because
- 1 times m-reduction [i] would yield (6, 32, 2506)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 6278 536979 808100 032678 988487 034229 016111 069944 611125 060560 > 6432 [i]