Best Known (131, 238, s)-Nets in Base 2
(131, 238, 66)-Net over F2 — Constructive and digital
Digital (131, 238, 66)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 92, 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, 146, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2 (see above)
- digital (39, 92, 33)-net over F2, using
(131, 238, 82)-Net over F2 — Digital
Digital (131, 238, 82)-net over F2, using
(131, 238, 298)-Net in Base 2 — Upper bound on s
There is no (131, 238, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (131, 237, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2237, 299, S2, 106), but
- the linear programming bound shows that M ≥ 2 372623 864838 720824 144751 616230 912568 605364 469958 081012 522169 374458 839809 772727 298051 538944 / 10 001354 293176 388857 > 2237 [i]
- extracting embedded orthogonal array [i] would yield OA(2237, 299, S2, 106), but