Best Known (239−108, 239, s)-Nets in Base 2
(239−108, 239, 63)-Net over F2 — Constructive and digital
Digital (131, 239, 63)-net over F2, using
- 4 times m-reduction [i] based on digital (131, 243, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 77, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (54, 166, 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 (21, 77, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(239−108, 239, 81)-Net over F2 — Digital
Digital (131, 239, 81)-net over F2, using
- t-expansion [i] based on digital (126, 239, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(239−108, 239, 291)-Net in Base 2 — Upper bound on s
There is no (131, 239, 292)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2239, 292, S2, 108), but
- the linear programming bound shows that M ≥ 129 753212 264703 737764 759763 826530 014325 194921 459040 258227 297024 189374 782768 881401 211050 262528 / 138 951361 618522 578125 > 2239 [i]