Best Known (213−108, 213, s)-Nets in Base 2
(213−108, 213, 56)-Net over F2 — Constructive and digital
Digital (105, 213, 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]
(213−108, 213, 65)-Net over F2 — Digital
Digital (105, 213, 65)-net over F2, using
- t-expansion [i] based on digital (95, 213, 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
(213−108, 213, 221)-Net in Base 2 — Upper bound on s
There is no (105, 213, 222)-net in base 2, because
- 4 times m-reduction [i] would yield (105, 209, 222)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2209, 222, S2, 104), but
- the linear programming bound shows that M ≥ 18 376994 896163 229078 786695 830800 490439 647194 147395 819913 877265 580032 / 16165 > 2209 [i]
- extracting embedded orthogonal array [i] would yield OA(2209, 222, S2, 104), but