Best Known (20, 66, s)-Nets in Base 16
(20, 66, 65)-Net over F16 — Constructive and digital
Digital (20, 66, 65)-net over F16, using
- t-expansion [i] based on digital (6, 66, 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
(20, 66, 76)-Net in Base 16 — Constructive
(20, 66, 76)-net in base 16, using
- 9 times m-reduction [i] based on (20, 75, 76)-net in base 16, using
- base change [i] based on digital (5, 60, 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, 60, 76)-net over F32, using
(20, 66, 129)-Net over F16 — Digital
Digital (20, 66, 129)-net over F16, using
- t-expansion [i] based on digital (19, 66, 129)-net over F16, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 19 and N(F) ≥ 129, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
(20, 66, 1780)-Net in Base 16 — Upper bound on s
There is no (20, 66, 1781)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 29 702841 716905 264701 240424 295933 110403 826828 180059 222733 590413 560517 793823 174496 > 1666 [i]