Best Known (71−45, 71, s)-Nets in Base 32
(71−45, 71, 120)-Net over F32 — Constructive and digital
Digital (26, 71, 120)-net over F32, using
- t-expansion [i] based on digital (11, 71, 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
(71−45, 71, 216)-Net in Base 32 — Constructive
(26, 71, 216)-net in base 32, using
- 1 times m-reduction [i] based on (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
- base change [i] based on (14, 60, 216)-net in base 64, using
(71−45, 71, 225)-Net over F32 — Digital
Digital (26, 71, 225)-net over F32, using
- t-expansion [i] based on digital (24, 71, 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
(71−45, 71, 257)-Net in Base 32
(26, 71, 257)-net in base 32, using
- 13 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
(71−45, 71, 17961)-Net in Base 32 — Upper bound on s
There is no (26, 71, 17962)-net in base 32, because
- 1 times m-reduction [i] would yield (26, 70, 17962)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2295 905182 219976 772646 894203 911304 075462 324380 398880 501020 287214 380868 178479 985900 763785 240369 456393 416952 > 3270 [i]