Best Known (5, 5+37, s)-Nets in Base 16
(5, 5+37, 49)-Net over F16 — Constructive and digital
Digital (5, 42, 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+37, 259)-Net in Base 16 — Upper bound on s
There is no (5, 42, 260)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1642, 260, S16, 37), but
- the linear programming bound shows that M ≥ 82546 838303 281237 578424 370992 091432 968896 156839 794322 944860 543934 254216 170212 093924 999168 / 216 231417 913583 229988 696738 554169 107343 > 1642 [i]