Best Known (40−28, 40, s)-Nets in Base 128
(40−28, 40, 288)-Net over F128 — Constructive and digital
Digital (12, 40, 288)-net over F128, using
- t-expansion [i] based on digital (9, 40, 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
(40−28, 40, 321)-Net over F128 — Digital
Digital (12, 40, 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
(40−28, 40, 49911)-Net in Base 128 — Upper bound on s
There is no (12, 40, 49912)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 943204 561630 432274 105389 509620 793979 850479 391463 207379 566380 106044 143435 004131 887674 > 12840 [i]