Best Known (2, 2+11, s)-Nets in Base 16
(2, 2+11, 33)-Net over F16 — Constructive and digital
Digital (2, 13, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
(2, 2+11, 132)-Net in Base 16 — Upper bound on s
There is no (2, 13, 133)-net in base 16, because
- 1 times m-reduction [i] would yield (2, 12, 133)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 287 142013 440976 > 1612 [i]
- extracting embedded orthogonal array [i] would yield OA(1612, 133, S16, 10), but
- the linear programming bound shows that M ≥ 2932 482690 444395 806720 / 10 212553 > 1612 [i]