Best Known (24, 24+41, s)-Nets in Base 32
(24, 24+41, 120)-Net over F32 — Constructive and digital
Digital (24, 65, 120)-net over F32, using
- t-expansion [i] based on digital (11, 65, 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
(24, 24+41, 216)-Net in Base 32 — Constructive
(24, 65, 216)-net in base 32, using
- 1 times m-reduction [i] based on (24, 66, 216)-net in base 32, using
- base change [i] based on (13, 55, 216)-net in base 64, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 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, 48, 216)-net over F128, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on (13, 55, 216)-net in base 64, using
(24, 24+41, 225)-Net over F32 — Digital
Digital (24, 65, 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
(24, 24+41, 257)-Net in Base 32
(24, 65, 257)-net in base 32, using
- 7 times m-reduction [i] based on (24, 72, 257)-net in base 32, using
- base change [i] based on digital (12, 60, 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, 60, 257)-net over F64, using
(24, 24+41, 17545)-Net in Base 32 — Upper bound on s
There is no (24, 65, 17546)-net in base 32, because
- 1 times m-reduction [i] would yield (24, 64, 17546)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 136445 778806 404311 078182 302990 208999 723095 198076 922882 128644 190540 822632 692039 288611 091395 246736 > 3264 [i]