Best Known (44−29, 44, s)-Nets in Base 128
(44−29, 44, 288)-Net over F128 — Constructive and digital
Digital (15, 44, 288)-net over F128, using
- t-expansion [i] based on digital (9, 44, 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
(44−29, 44, 386)-Net over F128 — Digital
Digital (15, 44, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
(44−29, 44, 513)-Net in Base 128
(15, 44, 513)-net in base 128, using
- 12 times m-reduction [i] based on (15, 56, 513)-net in base 128, using
- base change [i] based on digital (8, 49, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 49, 513)-net over F256, using
(44−29, 44, 141181)-Net in Base 128 — Upper bound on s
There is no (15, 44, 141182)-net in base 128, because
- 1 times m-reduction [i] would yield (15, 43, 141182)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 4 074168 864835 386510 513568 663455 165252 316886 775295 532615 865285 056164 798880 109188 739552 498872 > 12843 [i]