Best Known (104, 104+125, s)-Nets in Base 2
(104, 104+125, 55)-Net over F2 — Constructive and digital
Digital (104, 229, 55)-net over F2, using
- t-expansion [i] based on digital (100, 229, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(104, 104+125, 65)-Net over F2 — Digital
Digital (104, 229, 65)-net over F2, using
- t-expansion [i] based on digital (95, 229, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(104, 104+125, 218)-Net in Base 2 — Upper bound on s
There is no (104, 229, 219)-net in base 2, because
- 23 times m-reduction [i] would yield (104, 206, 219)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2206, 219, S2, 102), but
- the linear programming bound shows that M ≥ 78984 218751 417890 023438 520762 752824 239171 321550 411833 440733 233152 / 767 > 2206 [i]
- extracting embedded orthogonal array [i] would yield OA(2206, 219, S2, 102), but