Best Known (32, 32+75, s)-Nets in Base 16
(32, 32+75, 65)-Net over F16 — Constructive and digital
Digital (32, 107, 65)-net over F16, using
- t-expansion [i] based on digital (6, 107, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(32, 32+75, 104)-Net in Base 16 — Constructive
(32, 107, 104)-net in base 16, using
- 8 times m-reduction [i] based on (32, 115, 104)-net in base 16, using
- base change [i] based on digital (9, 92, 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
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 92, 104)-net over F32, using
(32, 32+75, 168)-Net over F16 — Digital
Digital (32, 107, 168)-net over F16, using
- t-expansion [i] based on digital (31, 107, 168)-net over F16, using
- net from sequence [i] based on digital (31, 167)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 31 and N(F) ≥ 168, using
- net from sequence [i] based on digital (31, 167)-sequence over F16, using
(32, 32+75, 2730)-Net in Base 16 — Upper bound on s
There is no (32, 107, 2731)-net in base 16, because
- 1 times m-reduction [i] would yield (32, 106, 2731)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 43 681359 156645 883979 429563 834835 971741 797989 328562 424217 930106 707518 832789 658065 382499 580437 208710 075224 717189 441612 173849 507556 > 16106 [i]