Best Known (120, 120+95, s)-Nets in Base 2
(120, 120+95, 62)-Net over F2 — Constructive and digital
Digital (120, 215, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 66, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- digital (54, 149, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (19, 66, 20)-net over F2, using
(120, 120+95, 78)-Net over F2 — Digital
Digital (120, 215, 78)-net over F2, using
(120, 120+95, 297)-Net in Base 2 — Upper bound on s
There is no (120, 215, 298)-net in base 2, because
- 1 times m-reduction [i] would yield (120, 214, 298)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2214, 298, S2, 94), but
- 1 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
- 1 times code embedding in larger space [i] would yield OA(2215, 299, S2, 94), but
- extracting embedded orthogonal array [i] would yield OA(2214, 298, S2, 94), but