Best Known (125, 228, s)-Nets in Base 2
(125, 228, 62)-Net over F2 — Constructive and digital
Digital (125, 228, 62)-net over F2, using
- 1 times m-reduction [i] based on digital (125, 229, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 71, 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, 158, 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, 71, 20)-net over F2, using
- (u, u+v)-construction [i] based on
(125, 228, 80)-Net over F2 — Digital
Digital (125, 228, 80)-net over F2, using
- t-expansion [i] based on digital (121, 228, 80)-net over F2, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 121 and N(F) ≥ 80, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
(125, 228, 283)-Net in Base 2 — Upper bound on s
There is no (125, 228, 284)-net in base 2, because
- 1 times m-reduction [i] would yield (125, 227, 284)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2227, 284, S2, 102), but
- adding a parity check bit [i] would yield OA(2228, 285, S2, 103), but
- the linear programming bound shows that M ≥ 4 034161 780580 224571 807834 810043 778367 016643 680872 935104 289259 268042 795950 972450 751656 230912 / 8986 311777 879741 102525 > 2228 [i]
- adding a parity check bit [i] would yield OA(2228, 285, S2, 103), but
- extracting embedded orthogonal array [i] would yield OA(2227, 284, S2, 102), but