Best Known (68−56, 68, s)-Nets in Base 128
(68−56, 68, 288)-Net over F128 — Constructive and digital
Digital (12, 68, 288)-net over F128, using
- t-expansion [i] based on digital (9, 68, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(68−56, 68, 321)-Net over F128 — Digital
Digital (12, 68, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(68−56, 68, 11646)-Net in Base 128 — Upper bound on s
There is no (12, 68, 11647)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 195285 928057 008205 779474 152006 514539 987474 225811 127738 114896 415778 172122 074520 042655 341988 976573 479581 444134 497445 287791 127941 663874 793581 302693 > 12868 [i]