Best Known (67−46, 67, s)-Nets in Base 128
(67−46, 67, 288)-Net over F128 — Constructive and digital
Digital (21, 67, 288)-net over F128, using
- t-expansion [i] based on digital (9, 67, 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
(67−46, 67, 386)-Net over F128 — Digital
Digital (21, 67, 386)-net over F128, using
- t-expansion [i] based on digital (15, 67, 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
(67−46, 67, 513)-Net in Base 128
(21, 67, 513)-net in base 128, using
- t-expansion [i] based on (17, 67, 513)-net in base 128, using
- 5 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
- 5 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(67−46, 67, 102093)-Net in Base 128 — Upper bound on s
There is no (21, 67, 102094)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1524 368864 556303 903717 309811 504000 337384 549636 117561 898040 781392 695338 230080 895399 722473 282765 837044 896593 931859 895286 873900 924580 176173 332720 > 12867 [i]