Best Known (222−102, 222, s)-Nets in Base 2
(222−102, 222, 59)-Net over F2 — Constructive and digital
Digital (120, 222, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 66, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- digital (54, 156, 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 (15, 66, 17)-net over F2, using
(222−102, 222, 73)-Net over F2 — Digital
Digital (120, 222, 73)-net over F2, using
- t-expansion [i] based on digital (114, 222, 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
(222−102, 222, 263)-Net in Base 2 — Upper bound on s
There is no (120, 222, 264)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2222, 264, S2, 102), but
- the linear programming bound shows that M ≥ 973 660907 288068 814907 798296 039066 371687 485445 127151 965045 607730 242901 618708 185088 / 120 348422 834913 > 2222 [i]