Best Known (17, 17+45, s)-Nets in Base 128
(17, 17+45, 288)-Net over F128 — Constructive and digital
Digital (17, 62, 288)-net over F128, using
- t-expansion [i] based on digital (9, 62, 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
(17, 17+45, 386)-Net over F128 — Digital
Digital (17, 62, 386)-net over F128, using
- t-expansion [i] based on digital (15, 62, 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
(17, 17+45, 513)-Net in Base 128
(17, 62, 513)-net in base 128, using
- 10 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
(17, 17+45, 49622)-Net in Base 128 — Upper bound on s
There is no (17, 62, 49623)-net in base 128, because
- 1 times m-reduction [i] would yield (17, 61, 49623)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 346 733944 433305 100266 290763 141729 193441 715685 093758 507436 658050 522366 850102 291722 818590 022552 039461 288722 587837 813727 498131 041637 > 12861 [i]