Best Known (4, 4+54, s)-Nets in Base 16
(4, 4+54, 45)-Net over F16 — Constructive and digital
Digital (4, 58, 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
(4, 4+54, 161)-Net in Base 16 — Upper bound on s
There is no (4, 58, 162)-net in base 16, because
- 1 times m-reduction [i] would yield (4, 57, 162)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1657, 162, S16, 53), but
- the linear programming bound shows that M ≥ 68 064421 429565 073444 218271 835894 641922 164860 485347 516307 210053 372020 760005 649821 389598 325485 862912 / 156271 290683 540696 273382 153697 > 1657 [i]
- extracting embedded orthogonal array [i] would yield OA(1657, 162, S16, 53), but