Best Known (13, 38, s)-Nets in Base 128
(13, 38, 288)-Net over F128 — Constructive and digital
Digital (13, 38, 288)-net over F128, using
- t-expansion [i] based on digital (9, 38, 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
(13, 38, 321)-Net over F128 — Digital
Digital (13, 38, 321)-net over F128, using
- t-expansion [i] based on digital (12, 38, 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
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(13, 38, 513)-Net in Base 128
(13, 38, 513)-net in base 128, using
- 2 times m-reduction [i] based on (13, 40, 513)-net in base 128, using
- base change [i] based on digital (8, 35, 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, 35, 513)-net over F256, using
(13, 38, 130848)-Net in Base 128 — Upper bound on s
There is no (13, 38, 130849)-net in base 128, because
- 1 times m-reduction [i] would yield (13, 37, 130849)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 926350 620156 389942 764733 621156 808465 826880 282442 454606 364741 555980 286179 267592 > 12837 [i]