Best Known (14, 14+39, s)-Nets in Base 16
(14, 14+39, 65)-Net over F16 — Constructive and digital
Digital (14, 53, 65)-net over F16, using
- t-expansion [i] based on digital (6, 53, 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
(14, 14+39, 97)-Net over F16 — Digital
Digital (14, 53, 97)-net over F16, using
- t-expansion [i] based on digital (13, 53, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
(14, 14+39, 1033)-Net in Base 16 — Upper bound on s
There is no (14, 53, 1034)-net in base 16, because
- 1 times m-reduction [i] would yield (14, 52, 1034)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 414 811923 495457 438044 862918 925490 768685 081033 347863 944459 714816 > 1652 [i]