Best Known (52−40, 52, s)-Nets in Base 128
(52−40, 52, 288)-Net over F128 — Constructive and digital
Digital (12, 52, 288)-net over F128, using
- t-expansion [i] based on digital (9, 52, 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
(52−40, 52, 321)-Net over F128 — Digital
Digital (12, 52, 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
(52−40, 52, 19680)-Net in Base 128 — Upper bound on s
There is no (12, 52, 19681)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 37 597048 236005 860826 779982 207166 076067 321463 757340 668417 208127 027642 281454 156831 223981 029052 083469 916989 580632 > 12852 [i]