Best Known (228−133, 228, s)-Nets in Base 2
(228−133, 228, 54)-Net over F2 — Constructive and digital
Digital (95, 228, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 5 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(228−133, 228, 65)-Net over F2 — Digital
Digital (95, 228, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
(228−133, 228, 190)-Net in Base 2 — Upper bound on s
There is no (95, 228, 191)-net in base 2, because
- 1 times m-reduction [i] would yield (95, 227, 191)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 229 528865 379771 864286 763671 018508 204192 041578 714043 221408 654509 870198 > 2227 [i]