Best Known (21, 21+24, s)-Nets in Base 16
(21, 21+24, 103)-Net over F16 — Constructive and digital
Digital (21, 45, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 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, 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 (3, 15, 38)-net over F16, using
(21, 21+24, 146)-Net over F16 — Digital
Digital (21, 45, 146)-net over F16, using
(21, 21+24, 150)-Net in Base 16 — Constructive
(21, 45, 150)-net in base 16, using
- base change [i] based on (6, 30, 150)-net in base 64, using
- 5 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
- 5 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
(21, 21+24, 161)-Net in Base 16
(21, 45, 161)-net in base 16, using
- base change [i] based on digital (6, 30, 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
(21, 21+24, 11547)-Net in Base 16 — Upper bound on s
There is no (21, 45, 11548)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 533491 606359 173307 273793 844718 694148 933401 817155 864116 > 1645 [i]