Best Known (20, 20+23, s)-Nets in Base 16
(20, 20+23, 103)-Net over F16 — Constructive and digital
Digital (20, 43, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (6, 29, 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 (3, 14, 38)-net over F16, using
(20, 20+23, 140)-Net over F16 — Digital
Digital (20, 43, 140)-net over F16, using
(20, 20+23, 150)-Net in Base 16 — Constructive
(20, 43, 150)-net in base 16, using
- 161 times duplication [i] based on (19, 42, 150)-net in base 16, using
- base change [i] based on digital (1, 24, 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, 24, 150)-net over F128, using
(20, 20+23, 12950)-Net in Base 16 — Upper bound on s
There is no (20, 43, 12951)-net in base 16, because
- 1 times m-reduction [i] would yield (20, 42, 12951)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 374 367900 260336 598278 772036 571299 875081 341563 737416 > 1642 [i]