Best Known (15−10, 15, s)-Nets in Base 16
(15−10, 15, 49)-Net over F16 — Constructive and digital
Digital (5, 15, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
(15−10, 15, 65)-Net in Base 16 — Constructive
(5, 15, 65)-net in base 16, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
(15−10, 15, 709)-Net in Base 16 — Upper bound on s
There is no (5, 15, 710)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 160604 015011 220751 > 1615 [i]