Best Known (234−124, 234, s)-Nets in Base 2
(234−124, 234, 57)-Net over F2 — Constructive and digital
Digital (110, 234, 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]
(234−124, 234, 72)-Net over F2 — Digital
Digital (110, 234, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
(234−124, 234, 230)-Net in Base 2 — Upper bound on s
There is no (110, 234, 231)-net in base 2, because
- 16 times m-reduction [i] would yield (110, 218, 231)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2218, 231, S2, 108), but
- the linear programming bound shows that M ≥ 5176 309760 092922 840576 066896 707769 089338 331729 127789 916371 893167 849472 / 11935 > 2218 [i]
- extracting embedded orthogonal array [i] would yield OA(2218, 231, S2, 108), but