Best Known (50, 50+137, s)-Nets in Base 2
(50, 50+137, 35)-Net over F2 — Constructive and digital
Digital (50, 187, 35)-net over F2, using
- t-expansion [i] based on digital (48, 187, 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, 50+137, 40)-Net over F2 — Digital
Digital (50, 187, 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, 50+137, 75)-Net in Base 2 — Upper bound on s
There is no (50, 187, 76)-net in base 2, because
- 42 times m-reduction [i] would yield (50, 145, 76)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2145, 76, S2, 2, 95), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 178 405961 588244 985132 285746 181186 892047 843328 / 3 > 2145 [i]
- extracting embedded OOA [i] would yield OOA(2145, 76, S2, 2, 95), but