Best Known (133, 133+110, s)-Nets in Base 2
(133, 133+110, 66)-Net over F2 — Constructive and digital
Digital (133, 243, 66)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 94, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (39, 149, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2 (see above)
- digital (39, 94, 33)-net over F2, using
(133, 133+110, 82)-Net over F2 — Digital
Digital (133, 243, 82)-net over F2, using
(133, 133+110, 298)-Net in Base 2 — Upper bound on s
There is no (133, 243, 299)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2243, 299, S2, 110), but
- 1 times code embedding in larger space [i] would yield OA(2244, 300, S2, 110), but
- the linear programming bound shows that M ≥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2244 [i]
- 1 times code embedding in larger space [i] would yield OA(2244, 300, S2, 110), but