Best Known (18−12, 18, s)-Nets in Base 16
(18−12, 18, 65)-Net over F16 — Constructive and digital
Digital (6, 18, 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
(18−12, 18, 814)-Net in Base 16 — Upper bound on s
There is no (6, 18, 815)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 4735 943135 263418 990851 > 1618 [i]