Best Known (46−24, 46, s)-Nets in Base 16
(46−24, 46, 110)-Net over F16 — Constructive and digital
Digital (22, 46, 110)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- digital (6, 30, 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
- digital (4, 16, 45)-net over F16, using
(46−24, 46, 150)-Net in Base 16 — Constructive
(22, 46, 150)-net in base 16, using
- 3 times m-reduction [i] based on (22, 49, 150)-net in base 16, using
- base change [i] based on digital (1, 28, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 28, 150)-net over F128, using
(46−24, 46, 166)-Net over F16 — Digital
Digital (22, 46, 166)-net over F16, using
(46−24, 46, 14550)-Net in Base 16 — Upper bound on s
There is no (22, 46, 14551)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 24 531712 608206 156528 662884 222503 531544 690779 960313 993406 > 1646 [i]