Best Known (36−25, 36, s)-Nets in Base 16
(36−25, 36, 65)-Net over F16 — Constructive and digital
Digital (11, 36, 65)-net over F16, using
- t-expansion [i] based on digital (6, 36, 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
(36−25, 36, 81)-Net over F16 — Digital
Digital (11, 36, 81)-net over F16, using
- t-expansion [i] based on digital (10, 36, 81)-net over F16, using
- net from sequence [i] based on digital (10, 80)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 10 and N(F) ≥ 81, using
- net from sequence [i] based on digital (10, 80)-sequence over F16, using
(36−25, 36, 1139)-Net in Base 16 — Upper bound on s
There is no (11, 36, 1140)-net in base 16, because
- 1 times m-reduction [i] would yield (11, 35, 1140)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 394104 945866 449427 564931 980504 254062 734076 > 1635 [i]