Best Known (69−34, 69, s)-Nets in Base 2
(69−34, 69, 24)-Net over F2 — Constructive and digital
Digital (35, 69, 24)-net over F2, using
- t-expansion [i] based on digital (33, 69, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(69−34, 69, 29)-Net over F2 — Digital
Digital (35, 69, 29)-net over F2, using
- net from sequence [i] based on digital (35, 28)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 35 and N(F) ≥ 29, using
(69−34, 69, 83)-Net over F2 — Upper bound on s (digital)
There is no digital (35, 69, 84)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(269, 84, F2, 34) (dual of [84, 15, 35]-code), but
(69−34, 69, 84)-Net in Base 2 — Upper bound on s
There is no (35, 69, 85)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(269, 85, S2, 34), but
- the linear programming bound shows that M ≥ 302231 454903 657293 676544 / 429 > 269 [i]