Best Known (7, 7+101, s)-Nets in Base 16
(7, 7+101, 65)-Net over F16 — Constructive and digital
Digital (7, 108, 65)-net over F16, using
- t-expansion [i] based on digital (6, 108, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(7, 7+101, 136)-Net in Base 16 — Upper bound on s
There is no (7, 108, 137)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16108, 137, S16, 101), but
- the linear programming bound shows that M ≥ 118736 773014 208616 177723 879613 831529 334795 458441 916218 266743 421653 715775 366917 101838 158985 419553 677902 330671 598987 941566 420090 543843 172125 117312 401408 / 10 241228 302007 287923 > 16108 [i]