Best Known (88−36, 88, s)-Nets in Base 16
(88−36, 88, 530)-Net over F16 — Constructive and digital
Digital (52, 88, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 44, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(88−36, 88, 1026)-Net over F16 — Digital
Digital (52, 88, 1026)-net over F16, using
- trace code for nets [i] based on digital (8, 44, 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
(88−36, 88, 388004)-Net in Base 16 — Upper bound on s
There is no (52, 88, 388005)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 9174 214023 560780 911691 257373 608024 183525 981271 180771 682387 062622 856148 202369 272730 289497 837005 362014 911476 > 1688 [i]