Best Known (71−52, 71, s)-Nets in Base 128
(71−52, 71, 288)-Net over F128 — Constructive and digital
Digital (19, 71, 288)-net over F128, using
- t-expansion [i] based on digital (9, 71, 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
(71−52, 71, 386)-Net over F128 — Digital
Digital (19, 71, 386)-net over F128, using
- t-expansion [i] based on digital (15, 71, 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
(71−52, 71, 513)-Net in Base 128
(19, 71, 513)-net in base 128, using
- t-expansion [i] based on (17, 71, 513)-net in base 128, using
- 1 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
- 1 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(71−52, 71, 47171)-Net in Base 128 — Upper bound on s
There is no (19, 71, 47172)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 409364 185955 216175 707292 208687 780850 360963 034267 825680 697117 306305 543537 712294 262356 969099 453565 175851 977909 184168 577457 305756 944854 860434 767979 775800 > 12871 [i]