Best Known (4, 4+64, s)-Nets in Base 128
(4, 4+64, 192)-Net over F128 — Constructive and digital
Digital (4, 68, 192)-net over F128, using
- t-expansion [i] based on digital (3, 68, 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+64, 215)-Net over F128 — Digital
Digital (4, 68, 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+64, 2811)-Net in Base 128 — Upper bound on s
There is no (4, 68, 2812)-net in base 128, because
- 20 times m-reduction [i] would yield (4, 48, 2812)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 140417 822584 071944 770460 154931 018936 977601 663247 674921 957406 554173 074207 475708 863843 188087 852394 403654 > 12848 [i]