Best Known (15, 15+32, s)-Nets in Base 128
(15, 15+32, 288)-Net over F128 — Constructive and digital
Digital (15, 47, 288)-net over F128, using
- t-expansion [i] based on digital (9, 47, 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
(15, 15+32, 386)-Net over F128 — Digital
Digital (15, 47, 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
(15, 15+32, 513)-Net in Base 128
(15, 47, 513)-net in base 128, using
- 9 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
(15, 15+32, 82913)-Net in Base 128 — Upper bound on s
There is no (15, 47, 82914)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1093 767163 356706 169989 068872 030083 600239 321921 105045 311525 143966 491840 773494 755919 004375 455818 879914 > 12847 [i]