Best Known (21, 33, s)-Nets in Base 16
(21, 33, 552)-Net over F16 — Constructive and digital
Digital (21, 33, 552)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 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 (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 12, 257)-net over F256, using
- digital (3, 9, 38)-net over F16, using
(21, 33, 579)-Net in Base 16 — Constructive
(21, 33, 579)-net in base 16, using
- (u, u+v)-construction [i] based on
- (3, 9, 65)-net in base 16, using
- base change [i] based on digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 6, 65)-net over F64, using
- digital (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 12, 257)-net over F256, using
- (3, 9, 65)-net in base 16, using
(21, 33, 1346)-Net over F16 — Digital
Digital (21, 33, 1346)-net over F16, using
(21, 33, 837122)-Net in Base 16 — Upper bound on s
There is no (21, 33, 837123)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 5444 521674 216337 618820 884345 332842 125696 > 1633 [i]