Best Known (39−26, 39, s)-Nets in Base 16
(39−26, 39, 65)-Net over F16 — Constructive and digital
Digital (13, 39, 65)-net over F16, using
- t-expansion [i] based on digital (6, 39, 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
(39−26, 39, 76)-Net in Base 16 — Constructive
(13, 39, 76)-net in base 16, using
- 1 times m-reduction [i] based on (13, 40, 76)-net in base 16, using
- base change [i] based on digital (5, 32, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 32, 76)-net over F32, using
(39−26, 39, 97)-Net over F16 — Digital
Digital (13, 39, 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
(39−26, 39, 1540)-Net in Base 16 — Upper bound on s
There is no (13, 39, 1541)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 91498 219230 181997 117749 990966 853661 105422 711296 > 1639 [i]