Best Known (87−60, 87, s)-Nets in Base 32
(87−60, 87, 120)-Net over F32 — Constructive and digital
Digital (27, 87, 120)-net over F32, using
- t-expansion [i] based on digital (11, 87, 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
(87−60, 87, 177)-Net in Base 32 — Constructive
(27, 87, 177)-net in base 32, using
- t-expansion [i] based on (25, 87, 177)-net in base 32, using
- 21 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- 21 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
(87−60, 87, 225)-Net over F32 — Digital
Digital (27, 87, 225)-net over F32, using
- t-expansion [i] based on digital (24, 87, 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
(87−60, 87, 257)-Net in Base 32
(27, 87, 257)-net in base 32, using
- 3 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
(87−60, 87, 8987)-Net in Base 32 — Upper bound on s
There is no (27, 87, 8988)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 89017 784442 808295 032528 898045 294282 452776 909126 098102 296261 017060 082885 282182 562750 391649 525919 914375 946073 354013 579193 645940 243904 > 3287 [i]