Best Known (119, 119+106, s)-Nets in Base 2
(119, 119+106, 57)-Net over F2 — Constructive and digital
Digital (119, 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
(119, 119+106, 73)-Net over F2 — Digital
Digital (119, 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
(119, 119+106, 255)-Net in Base 2 — Upper bound on s
There is no (119, 225, 256)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2225, 256, S2, 106), but
- the linear programming bound shows that M ≥ 4 533712 341462 452600 463527 949755 696668 157794 361414 843709 255199 826856 399742 173184 / 59446 678005 > 2225 [i]