Best Known (21, 21+55, s)-Nets in Base 128
(21, 21+55, 288)-Net over F128 — Constructive and digital
Digital (21, 76, 288)-net over F128, using
- t-expansion [i] based on digital (9, 76, 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
(21, 21+55, 386)-Net over F128 — Digital
Digital (21, 76, 386)-net over F128, using
- t-expansion [i] based on digital (15, 76, 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
(21, 21+55, 513)-Net in Base 128
(21, 76, 513)-net in base 128, using
- 1284 times duplication [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
(21, 21+55, 61357)-Net in Base 128 — Upper bound on s
There is no (21, 76, 61358)-net in base 128, because
- 1 times m-reduction [i] would yield (21, 75, 61358)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 109 841028 051011 830476 142240 651045 289877 067800 072729 461794 868793 432075 908968 753058 974385 898251 701818 007908 253892 766170 855559 902870 769959 922598 902445 233810 979092 > 12875 [i]