Best Known (53, 53+51, s)-Nets in Base 2
(53, 53+51, 36)-Net over F2 — Constructive and digital
Digital (53, 104, 36)-net over F2, using
- t-expansion [i] based on digital (51, 104, 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
(53, 53+51, 40)-Net over F2 — Digital
Digital (53, 104, 40)-net over F2, using
- t-expansion [i] based on digital (50, 104, 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
(53, 53+51, 120)-Net in Base 2 — Upper bound on s
There is no (53, 104, 121)-net in base 2, because
- 1 times m-reduction [i] would yield (53, 103, 121)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2103, 121, S2, 50), but
- the linear programming bound shows that M ≥ 2 256052 985033 382604 596500 655046 131712 / 211575 > 2103 [i]
- extracting embedded orthogonal array [i] would yield OA(2103, 121, S2, 50), but