Best Known (70−46, 70, s)-Nets in Base 32
(70−46, 70, 120)-Net over F32 — Constructive and digital
Digital (24, 70, 120)-net over F32, using
- t-expansion [i] based on digital (11, 70, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(70−46, 70, 192)-Net in Base 32 — Constructive
(24, 70, 192)-net in base 32, using
- 2 times m-reduction [i] based on (24, 72, 192)-net in base 32, using
- base change [i] based on (12, 60, 192)-net in base 64, using
- 3 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- base change [i] based on digital (3, 54, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 54, 192)-net over F128, using
- 3 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- base change [i] based on (12, 60, 192)-net in base 64, using
(70−46, 70, 225)-Net over F32 — Digital
Digital (24, 70, 225)-net over F32, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
(70−46, 70, 257)-Net in Base 32
(24, 70, 257)-net in base 32, using
- 2 times m-reduction [i] based on (24, 72, 257)-net in base 32, using
- base change [i] based on digital (12, 60, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 60, 257)-net over F64, using
(70−46, 70, 11575)-Net in Base 32 — Upper bound on s
There is no (24, 70, 11576)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2295 065078 548954 086971 107505 114092 671221 903822 524365 905956 765845 134929 124253 422456 686669 677397 928205 994633 > 3270 [i]