Best Known (5, 5+42, s)-Nets in Base 16
(5, 5+42, 49)-Net over F16 — Constructive and digital
Digital (5, 47, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
(5, 5+42, 258)-Net in Base 16 — Upper bound on s
There is no (5, 47, 259)-net in base 16, because
- 3 times m-reduction [i] would yield (5, 44, 259)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1644, 259, S16, 39), but
- the linear programming bound shows that M ≥ 50 774228 000133 379999 225829 635218 451511 707870 599888 076338 819166 895840 828939 967031 893032 960000 / 526 270836 757774 539017 306203 501343 024669 > 1644 [i]
- extracting embedded orthogonal array [i] would yield OA(1644, 259, S16, 39), but