Best Known (16, 16+39, s)-Nets in Base 128
(16, 16+39, 288)-Net over F128 — Constructive and digital
Digital (16, 55, 288)-net over F128, using
- t-expansion [i] based on digital (9, 55, 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
(16, 16+39, 386)-Net over F128 — Digital
Digital (16, 55, 386)-net over F128, using
- t-expansion [i] based on digital (15, 55, 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
(16, 16+39, 513)-Net in Base 128
(16, 55, 513)-net in base 128, using
- 9 times m-reduction [i] based on (16, 64, 513)-net in base 128, using
- base change [i] based on digital (8, 56, 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, 56, 513)-net over F256, using
(16, 16+39, 60849)-Net in Base 128 — Upper bound on s
There is no (16, 55, 60850)-net in base 128, because
- 1 times m-reduction [i] would yield (16, 54, 60850)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 615698 014385 605641 412137 207407 605478 284218 944501 176912 779107 178707 571139 159881 763283 159480 192137 101383 363939 537936 > 12854 [i]