Best Known (72−46, 72, s)-Nets in Base 32
(72−46, 72, 120)-Net over F32 — Constructive and digital
Digital (26, 72, 120)-net over F32, using
- t-expansion [i] based on digital (11, 72, 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
(72−46, 72, 216)-Net in Base 32 — Constructive
(26, 72, 216)-net in base 32, using
- base change [i] based on (14, 60, 216)-net in base 64, using
- 3 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- 3 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
(72−46, 72, 225)-Net over F32 — Digital
Digital (26, 72, 225)-net over F32, using
- t-expansion [i] based on digital (24, 72, 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
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
(72−46, 72, 257)-Net in Base 32
(26, 72, 257)-net in base 32, using
- 12 times m-reduction [i] based on (26, 84, 257)-net in base 32, using
- base change [i] based on digital (12, 70, 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, 70, 257)-net over F64, using
(72−46, 72, 15651)-Net in Base 32 — Upper bound on s
There is no (26, 72, 15652)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 351907 501714 900877 706142 620979 865250 012692 242733 019076 672508 901542 009075 679423 701114 201260 091067 396149 234280 > 3272 [i]