Best Known (202−95, 202, s)-Nets in Base 2
(202−95, 202, 56)-Net over F2 — Constructive and digital
Digital (107, 202, 56)-net over F2, using
- t-expansion [i] based on digital (105, 202, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 7 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
(202−95, 202, 65)-Net over F2 — Digital
Digital (107, 202, 65)-net over F2, using
- t-expansion [i] based on digital (95, 202, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(202−95, 202, 284)-Net in Base 2 — Upper bound on s
There is no (107, 202, 285)-net in base 2, because
- 1 times m-reduction [i] would yield (107, 201, 285)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2201, 285, S2, 94), but
- 14 times code embedding in larger space [i] would yield OA(2215, 299, S2, 94), but
- adding a parity check bit [i] would yield OA(2216, 300, S2, 95), but
- the linear programming bound shows that M ≥ 872407 680551 113098 866799 953294 886066 311827 924058 628412 428016 149220 115296 187426 023936 653562 740736 / 5 938078 052347 021578 779474 608305 > 2216 [i]
- adding a parity check bit [i] would yield OA(2216, 300, S2, 95), but
- 14 times code embedding in larger space [i] would yield OA(2215, 299, S2, 94), but
- extracting embedded orthogonal array [i] would yield OA(2201, 285, S2, 94), but