Best Known (30−21, 30, s)-Nets in Base 32
(30−21, 30, 104)-Net over F32 — Constructive and digital
Digital (9, 30, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
(30−21, 30, 108)-Net over F32 — Digital
Digital (9, 30, 108)-net over F32, using
- net from sequence [i] based on digital (9, 107)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 108, using
(30−21, 30, 129)-Net in Base 32 — Constructive
(9, 30, 129)-net in base 32, using
- base change [i] based on (4, 25, 129)-net in base 64, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
(30−21, 30, 3380)-Net in Base 32 — Upper bound on s
There is no (9, 30, 3381)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 29, 3381)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 44 719171 206942 200190 241710 594251 828901 165788 > 3229 [i]