Best Known (43−39, 43, s)-Nets in Base 128
(43−39, 43, 192)-Net over F128 — Constructive and digital
Digital (4, 43, 192)-net over F128, using
- t-expansion [i] based on digital (3, 43, 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
(43−39, 43, 215)-Net over F128 — Digital
Digital (4, 43, 215)-net over F128, using
- net from sequence [i] based on digital (4, 214)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 4 and N(F) ≥ 215, using
(43−39, 43, 2831)-Net in Base 128 — Upper bound on s
There is no (4, 43, 2832)-net in base 128, because
- 1 times m-reduction [i] would yield (4, 42, 2832)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 31882 129028 731779 622030 549112 515271 262935 514707 154152 275145 070359 691949 095370 979772 546352 > 12842 [i]