Best Known (61−52, 61, s)-Nets in Base 16
(61−52, 61, 65)-Net over F16 — Constructive and digital
Digital (9, 61, 65)-net over F16, using
- t-expansion [i] based on digital (6, 61, 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
(61−52, 61, 72)-Net over F16 — Digital
Digital (9, 61, 72)-net over F16, using
- net from sequence [i] based on digital (9, 71)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
(61−52, 61, 456)-Net in Base 16 — Upper bound on s
There is no (9, 61, 457)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 29 806131 810879 548955 365141 972866 485624 594032 333861 044687 052861 245819 653856 > 1661 [i]