Best Known (209−94, 209, s)-Nets in Base 2
(209−94, 209, 57)-Net over F2 — Constructive and digital
Digital (115, 209, 57)-net over F2, using
- t-expansion [i] based on digital (110, 209, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(209−94, 209, 73)-Net over F2 — Digital
Digital (115, 209, 73)-net over F2, using
- t-expansion [i] based on digital (114, 209, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(209−94, 209, 292)-Net in Base 2 — Upper bound on s
There is no (115, 209, 293)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2209, 293, S2, 94), but
- 6 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
- 6 times code embedding in larger space [i] would yield OA(2215, 299, S2, 94), but