Best Known (37−33, 37, s)-Nets in Base 16
(37−33, 37, 45)-Net over F16 — Constructive and digital
Digital (4, 37, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
(37−33, 37, 211)-Net in Base 16 — Upper bound on s
There is no (4, 37, 212)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1637, 212, S16, 33), but
- the linear programming bound shows that M ≥ 1 547409 487131 714899 677390 885780 847200 380117 291059 645539 158964 829585 839627 436032 / 4303 201222 842834 783226 830613 131997 > 1637 [i]