Best Known (12, 39, s)-Nets in Base 128
(12, 39, 288)-Net over F128 — Constructive and digital
Digital (12, 39, 288)-net over F128, using
- t-expansion [i] based on digital (9, 39, 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
(12, 39, 321)-Net over F128 — Digital
Digital (12, 39, 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
(12, 39, 64431)-Net in Base 128 — Upper bound on s
There is no (12, 39, 64432)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 38, 64432)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 118 583345 018780 962231 722747 063872 712377 843762 252896 040720 985609 372867 177145 887891 > 12838 [i]