Best Known (120, 225, s)-Nets in Base 2
(120, 225, 57)-Net over F2 — Constructive and digital
Digital (120, 225, 57)-net over F2, using
- t-expansion [i] based on digital (110, 225, 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
(120, 225, 73)-Net over F2 — Digital
Digital (120, 225, 73)-net over F2, using
- t-expansion [i] based on digital (114, 225, 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
(120, 225, 260)-Net in Base 2 — Upper bound on s
There is no (120, 225, 261)-net in base 2, because
- 1 times m-reduction [i] would yield (120, 224, 261)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2224, 261, S2, 104), but
- the linear programming bound shows that M ≥ 3 110164 158296 245315 038857 848709 549303 901423 162182 003510 964453 682176 680102 199296 / 86817 637125 > 2224 [i]
- extracting embedded orthogonal array [i] would yield OA(2224, 261, S2, 104), but