Best Known (14, 14+29, s)-Nets in Base 128
(14, 14+29, 288)-Net over F128 — Constructive and digital
Digital (14, 43, 288)-net over F128, using
- t-expansion [i] based on digital (9, 43, 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
(14, 14+29, 353)-Net over F128 — Digital
Digital (14, 43, 353)-net over F128, using
- net from sequence [i] based on digital (14, 352)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 14 and N(F) ≥ 353, using
(14, 14+29, 513)-Net in Base 128
(14, 43, 513)-net in base 128, using
- 5 times m-reduction [i] based on (14, 48, 513)-net in base 128, using
- base change [i] based on digital (8, 42, 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, 42, 513)-net over F256, using
(14, 14+29, 99828)-Net in Base 128 — Upper bound on s
There is no (14, 43, 99829)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 42, 99829)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 31830 276558 691304 449088 413063 649403 619069 532011 928073 340714 318890 970952 634753 731390 025912 > 12842 [i]