Best Known (19−12, 19, s)-Nets in Base 16
(19−12, 19, 65)-Net over F16 — Constructive and digital
Digital (7, 19, 65)-net over F16, using
- t-expansion [i] based on digital (6, 19, 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
(19−12, 19, 1294)-Net in Base 16 — Upper bound on s
There is no (7, 19, 1295)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 75623 809097 588652 769051 > 1619 [i]