Best Known (106, 106+103, s)-Nets in Base 2
(106, 106+103, 56)-Net over F2 — Constructive and digital
Digital (106, 209, 56)-net over F2, using
- t-expansion [i] based on digital (105, 209, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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 (105, 55)-sequence over F2, using
(106, 106+103, 65)-Net over F2 — Digital
Digital (106, 209, 65)-net over F2, using
- t-expansion [i] based on digital (95, 209, 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
(106, 106+103, 224)-Net in Base 2 — Upper bound on s
There is no (106, 209, 225)-net in base 2, because
- 3 times m-reduction [i] would yield (106, 206, 225)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2206, 225, S2, 100), but
- the linear programming bound shows that M ≥ 46 910043 920112 941849 753861 456344 948196 047834 057482 094744 342146 056192 / 365313 > 2206 [i]
- extracting embedded orthogonal array [i] would yield OA(2206, 225, S2, 100), but