Best Known (4, 4+31, s)-Nets in Base 128
(4, 4+31, 192)-Net over F128 — Constructive and digital
Digital (4, 35, 192)-net over F128, using
- t-expansion [i] based on digital (3, 35, 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+31, 215)-Net over F128 — Digital
Digital (4, 35, 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+31, 3014)-Net in Base 128 — Upper bound on s
There is no (4, 35, 3015)-net in base 128, because
- 1 times m-reduction [i] would yield (4, 34, 3015)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 441794 651253 097164 421389 295380 566056 682620 097281 692745 010182 614196 320576 > 12834 [i]