Best Known (6, 6+88, s)-Nets in Base 16
(6, 6+88, 65)-Net over F16 — Constructive and digital
Digital (6, 94, 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
(6, 6+88, 141)-Net in Base 16 — Upper bound on s
There is no (6, 94, 142)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1694, 142, S16, 88), but
- the linear programming bound shows that M ≥ 1687 479299 101835 757745 542921 117930 118967 179396 325435 251904 588658 355450 969583 020587 777608 792300 759257 925321 751672 900933 080073 844715 159552 / 10602 340405 608126 556073 > 1694 [i]