Best Known (226−75, 226, s)-Nets in Base 2
(226−75, 226, 112)-Net over F2 — Constructive and digital
Digital (151, 226, 112)-net over F2, using
- 10 times m-reduction [i] based on digital (151, 236, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 118, 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
- trace code for nets [i] based on digital (33, 118, 56)-net over F4, using
(226−75, 226, 157)-Net over F2 — Digital
Digital (151, 226, 157)-net over F2, using
(226−75, 226, 938)-Net in Base 2 — Upper bound on s
There is no (151, 226, 939)-net in base 2, because
- 1 times m-reduction [i] would yield (151, 225, 939)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 55 290167 135959 832626 731776 752679 409879 050297 769868 015232 449686 090048 > 2225 [i]