Best Known (3, 3+27, s)-Nets in Base 16
(3, 3+27, 38)-Net over F16 — Constructive and digital
Digital (3, 30, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
(3, 3+27, 170)-Net in Base 16 — Upper bound on s
There is no (3, 30, 171)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1630, 171, S16, 27), but
- the linear programming bound shows that M ≥ 1 692948 843458 152892 108119 879540 787513 074799 322665 724661 465088 / 1 215785 540371 935606 103343 > 1630 [i]