Best Known (23, 23+41, s)-Nets in Base 32
(23, 23+41, 120)-Net over F32 — Constructive and digital
Digital (23, 64, 120)-net over F32, using
- t-expansion [i] based on digital (11, 64, 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
(23, 23+41, 185)-Net over F32 — Digital
Digital (23, 64, 185)-net over F32, using
- t-expansion [i] based on digital (21, 64, 185)-net over F32, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 21 and N(F) ≥ 185, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
(23, 23+41, 192)-Net in Base 32 — Constructive
(23, 64, 192)-net in base 32, using
- 6 times m-reduction [i] based on (23, 70, 192)-net in base 32, using
- base change [i] based on digital (3, 50, 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, 50, 192)-net over F128, using
(23, 23+41, 257)-Net in Base 32
(23, 64, 257)-net in base 32, using
- 2 times m-reduction [i] based on (23, 66, 257)-net in base 32, using
- base change [i] based on digital (12, 55, 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, 55, 257)-net over F64, using
(23, 23+41, 14752)-Net in Base 32 — Upper bound on s
There is no (23, 64, 14753)-net in base 32, because
- 1 times m-reduction [i] would yield (23, 63, 14753)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 66786 109671 464546 018072 570042 476961 425129 926039 856236 123746 914417 582949 348076 590462 005493 505256 > 3263 [i]