Best Known (27−21, 27, s)-Nets in Base 64
(27−21, 27, 128)-Net over F64 — Constructive and digital
Digital (6, 27, 128)-net over F64, using
- t-expansion [i] based on digital (5, 27, 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
(27−21, 27, 150)-Net in Base 64 — Constructive
(6, 27, 150)-net in base 64, using
- 8 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
(27−21, 27, 161)-Net over F64 — Digital
Digital (6, 27, 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
(27−21, 27, 172)-Net in Base 64
(6, 27, 172)-net in base 64, using
- 1 times m-reduction [i] based on (6, 28, 172)-net in base 64, using
- base change [i] based on digital (2, 24, 172)-net over F128, using
- net from sequence [i] based on digital (2, 171)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 2 and N(F) ≥ 172, using
- net from sequence [i] based on digital (2, 171)-sequence over F128, using
- base change [i] based on digital (2, 24, 172)-net over F128, using
(27−21, 27, 3565)-Net in Base 64 — Upper bound on s
There is no (6, 27, 3566)-net in base 64, because
- 1 times m-reduction [i] would yield (6, 26, 3566)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 91437 480183 167207 649887 537645 999877 685429 832230 > 6426 [i]