Best Known (51−34, 51, s)-Nets in Base 128
(51−34, 51, 288)-Net over F128 — Constructive and digital
Digital (17, 51, 288)-net over F128, using
- t-expansion [i] based on digital (9, 51, 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
(51−34, 51, 386)-Net over F128 — Digital
Digital (17, 51, 386)-net over F128, using
- t-expansion [i] based on digital (15, 51, 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
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(51−34, 51, 513)-Net in Base 128
(17, 51, 513)-net in base 128, using
- 21 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 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, 63, 513)-net over F256, using
(51−34, 51, 118506)-Net in Base 128 — Upper bound on s
There is no (17, 51, 118507)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 293595 589747 847044 171644 744625 844968 366071 743277 124422 376603 720011 714004 009959 234120 787370 421208 895048 222836 > 12851 [i]