Best Known (39−26, 39, s)-Nets in Base 128
(39−26, 39, 288)-Net over F128 — Constructive and digital
Digital (13, 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
(39−26, 39, 321)-Net over F128 — Digital
Digital (13, 39, 321)-net over F128, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(39−26, 39, 513)-Net in Base 128
(13, 39, 513)-net in base 128, using
- 1 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
(39−26, 39, 93584)-Net in Base 128 — Upper bound on s
There is no (13, 39, 93585)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 15178 098449 643996 985713 690845 764397 687690 894575 232436 797161 475119 419759 851448 075856 > 12839 [i]