Best Known (54−48, 54, s)-Nets in Base 16
(54−48, 54, 65)-Net over F16 — Constructive and digital
Digital (6, 54, 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
(54−48, 54, 295)-Net in Base 16 — Upper bound on s
There is no (6, 54, 296)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1654, 296, S16, 48), but
- the linear programming bound shows that M ≥ 2011 513311 979455 090693 456515 091117 689450 538048 909609 410984 156573 157061 442837 217823 537316 650760 826335 413264 964177 100800 / 18955 427562 564953 215144 845626 114011 506597 907434 178531 > 1654 [i]