Best Known (258−96, 258, s)-Nets in Base 2
(258−96, 258, 112)-Net over F2 — Constructive and digital
Digital (162, 258, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 129, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(258−96, 258, 135)-Net over F2 — Digital
Digital (162, 258, 135)-net over F2, using
(258−96, 258, 709)-Net in Base 2 — Upper bound on s
There is no (162, 258, 710)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 489942 129255 156019 241778 402895 554653 576764 497395 327108 001299 663230 321337 433460 > 2258 [i]