Best Known (50−40, 50, s)-Nets in Base 128
(50−40, 50, 288)-Net over F128 — Constructive and digital
Digital (10, 50, 288)-net over F128, using
- t-expansion [i] based on digital (9, 50, 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
(50−40, 50, 296)-Net over F128 — Digital
Digital (10, 50, 296)-net over F128, using
- net from sequence [i] based on digital (10, 295)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 10 and N(F) ≥ 296, using
(50−40, 50, 321)-Net in Base 128
(10, 50, 321)-net in base 128, using
- 14 times m-reduction [i] based on (10, 64, 321)-net in base 128, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
(50−40, 50, 12111)-Net in Base 128 — Upper bound on s
There is no (10, 50, 12112)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 2297 147549 732028 738921 680481 522004 125884 022662 496545 661097 692945 787531 185716 101694 403876 648702 184385 078564 > 12850 [i]