Best Known (74−47, 74, s)-Nets in Base 32
(74−47, 74, 120)-Net over F32 — Constructive and digital
Digital (27, 74, 120)-net over F32, using
- t-expansion [i] based on digital (11, 74, 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
(74−47, 74, 216)-Net in Base 32 — Constructive
(27, 74, 216)-net in base 32, using
- 3 times m-reduction [i] based on (27, 77, 216)-net in base 32, using
- base change [i] based on digital (5, 55, 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, 55, 216)-net over F128, using
(74−47, 74, 225)-Net over F32 — Digital
Digital (27, 74, 225)-net over F32, using
- t-expansion [i] based on digital (24, 74, 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
(74−47, 74, 257)-Net in Base 32
(27, 74, 257)-net in base 32, using
- 16 times m-reduction [i] based on (27, 90, 257)-net in base 32, using
- base change [i] based on digital (12, 75, 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, 75, 257)-net over F64, using
(74−47, 74, 18198)-Net in Base 32 — Upper bound on s
There is no (27, 74, 18199)-net in base 32, because
- 1 times m-reduction [i] would yield (27, 73, 18199)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 75 224504 200172 092803 985614 234157 284042 016405 936484 303476 548811 049126 954237 508499 092462 480613 421821 840430 387168 > 3273 [i]