Best Known (58−43, 58, s)-Nets in Base 32
(58−43, 58, 120)-Net over F32 — Constructive and digital
Digital (15, 58, 120)-net over F32, using
- t-expansion [i] based on digital (11, 58, 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
(58−43, 58, 128)-Net in Base 32 — Constructive
(15, 58, 128)-net in base 32, using
- 2 times m-reduction [i] based on (15, 60, 128)-net in base 32, using
- base change [i] based on digital (5, 50, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- base change [i] based on digital (5, 50, 128)-net over F64, using
(58−43, 58, 158)-Net over F32 — Digital
Digital (15, 58, 158)-net over F32, using
- net from sequence [i] based on digital (15, 157)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
(58−43, 58, 3397)-Net in Base 32 — Upper bound on s
There is no (15, 58, 3398)-net in base 32, because
- 1 times m-reduction [i] would yield (15, 57, 3398)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 62 306845 944541 818850 458106 543986 743868 775814 091267 858698 236645 632375 702783 476165 528964 > 3257 [i]