Best Known (109−106, 109, s)-Nets in Base 16
(109−106, 109, 38)-Net over F16 — Constructive and digital
Digital (3, 109, 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
(109−106, 109, 64)-Net in Base 16 — Upper bound on s
There is no (3, 109, 65)-net in base 16, because
- 48 times m-reduction [i] would yield (3, 61, 65)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1661, 65, S16, 58), but
- the linear programming bound shows that M ≥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 1661 [i]
- extracting embedded orthogonal array [i] would yield OA(1661, 65, S16, 58), but