Best Known (20, 66, s)-Nets in Base 128
(20, 66, 288)-Net over F128 — Constructive and digital
Digital (20, 66, 288)-net over F128, using
- t-expansion [i] based on digital (9, 66, 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
(20, 66, 386)-Net over F128 — Digital
Digital (20, 66, 386)-net over F128, using
- t-expansion [i] based on digital (15, 66, 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
(20, 66, 513)-Net in Base 128
(20, 66, 513)-net in base 128, using
- t-expansion [i] based on (17, 66, 513)-net in base 128, using
- 6 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
- 6 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(20, 66, 82674)-Net in Base 128 — Upper bound on s
There is no (20, 66, 82675)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 11 911010 503495 659618 549951 805099 605306 204201 112332 930287 657366 483083 096972 431474 519620 672851 852968 326703 367748 023658 173453 370808 648225 925856 > 12866 [i]