Best Known (108−55, 108, s)-Nets in Base 2
(108−55, 108, 36)-Net over F2 — Constructive and digital
Digital (53, 108, 36)-net over F2, using
- t-expansion [i] based on digital (51, 108, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 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 (51, 35)-sequence over F2, using
(108−55, 108, 40)-Net over F2 — Digital
Digital (53, 108, 40)-net over F2, using
- t-expansion [i] based on digital (50, 108, 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
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
(108−55, 108, 117)-Net in Base 2 — Upper bound on s
There is no (53, 108, 118)-net in base 2, because
- 1 times m-reduction [i] would yield (53, 107, 118)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2107, 118, S2, 54), but
- the linear programming bound shows that M ≥ 6490 371073 168534 535663 120411 525120 / 33 > 2107 [i]
- extracting embedded orthogonal array [i] would yield OA(2107, 118, S2, 54), but