Best Known (50, 256, s)-Nets in Base 2
(50, 256, 35)-Net over F2 — Constructive and digital
Digital (50, 256, 35)-net over F2, using
- t-expansion [i] based on digital (48, 256, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
(50, 256, 40)-Net over F2 — Digital
Digital (50, 256, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
(50, 256, 61)-Net in Base 2 — Upper bound on s
There is no (50, 256, 62)-net in base 2, because
- 16 times m-reduction [i] would yield (50, 240, 62)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2240, 62, S2, 4, 190), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 508 851954 656174 686919 989680 213960 532558 315362 300178 259939 022585 972274 495488 / 191 > 2240 [i]
- extracting embedded OOA [i] would yield OOA(2240, 62, S2, 4, 190), but