Best Known (4, 4+33, s)-Nets in Base 128
(4, 4+33, 192)-Net over F128 — Constructive and digital
Digital (4, 37, 192)-net over F128, using
- t-expansion [i] based on digital (3, 37, 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
(4, 4+33, 215)-Net over F128 — Digital
Digital (4, 37, 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
(4, 4+33, 2943)-Net in Base 128 — Upper bound on s
There is no (4, 37, 2944)-net in base 128, because
- 1 times m-reduction [i] would yield (4, 36, 2944)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 7264 603369 709928 336584 271493 113541 787774 564071 545776 277777 463889 937192 039385 > 12836 [i]