Best Known (63−46, 63, s)-Nets in Base 128
(63−46, 63, 288)-Net over F128 — Constructive and digital
Digital (17, 63, 288)-net over F128, using
- t-expansion [i] based on digital (9, 63, 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
(63−46, 63, 386)-Net over F128 — Digital
Digital (17, 63, 386)-net over F128, using
- t-expansion [i] based on digital (15, 63, 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
(63−46, 63, 513)-Net in Base 128
(17, 63, 513)-net in base 128, using
- 9 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
(63−46, 63, 43900)-Net in Base 128 — Upper bound on s
There is no (17, 63, 43901)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 5 681280 520986 241879 307759 172797 743517 153399 836395 903893 996456 375770 259527 720237 267876 946062 104914 703143 232844 247257 658592 366586 526312 > 12863 [i]