Best Known (52−28, 52, s)-Nets in Base 16
(52−28, 52, 110)-Net over F16 — Constructive and digital
Digital (24, 52, 110)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 18, 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, 34, 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, 18, 45)-net over F16, using
(52−28, 52, 150)-Net in Base 16 — Constructive
(24, 52, 150)-net in base 16, using
- 161 times duplication [i] based on (23, 51, 150)-net in base 16, using
- base change [i] based on (6, 34, 150)-net in base 64, using
- 1 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 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, 30, 150)-net over F128, using
- 1 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on (6, 34, 150)-net in base 64, using
(52−28, 52, 152)-Net over F16 — Digital
Digital (24, 52, 152)-net over F16, using
(52−28, 52, 161)-Net in Base 16
(24, 52, 161)-net in base 16, using
- 2 times m-reduction [i] based on (24, 54, 161)-net in base 16, using
- base change [i] based on digital (6, 36, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- base change [i] based on digital (6, 36, 161)-net over F64, using
(52−28, 52, 11954)-Net in Base 16 — Upper bound on s
There is no (24, 52, 11955)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 411 473699 416007 449536 003606 693898 580845 545322 207882 174414 137676 > 1652 [i]