Best Known (58, 58+42, s)-Nets in Base 16
(58, 58+42, 530)-Net over F16 — Constructive and digital
Digital (58, 100, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 50, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(58, 58+42, 1026)-Net over F16 — Digital
Digital (58, 100, 1026)-net over F16, using
- trace code for nets [i] based on digital (8, 50, 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
(58, 58+42, 313538)-Net in Base 16 — Upper bound on s
There is no (58, 100, 313539)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 582421 135862 866292 930535 827089 537444 977311 284166 814003 116375 782499 629172 175710 492369 515650 679862 585058 287836 172625 213536 > 16100 [i]