Best Known (61, 61+63, s)-Nets in Base 2
(61, 61+63, 43)-Net over F2 — Constructive and digital
Digital (61, 124, 43)-net over F2, using
- t-expansion [i] based on digital (59, 124, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(61, 61+63, 133)-Net in Base 2 — Upper bound on s
There is no (61, 124, 134)-net in base 2, because
- 1 times m-reduction [i] would yield (61, 123, 134)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2123, 134, S2, 62), but
- the linear programming bound shows that M ≥ 2988 104534 524490 882287 758271 510214 606848 / 247 > 2123 [i]
- extracting embedded orthogonal array [i] would yield OA(2123, 134, S2, 62), but