Best Known (40−15, 40, s)-Nets in Base 16
(40−15, 40, 552)-Net over F16 — Constructive and digital
Digital (25, 40, 552)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 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 (15, 30, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 15, 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, 15, 257)-net over F256, using
- digital (3, 10, 38)-net over F16, using
(40−15, 40, 558)-Net in Base 16 — Constructive
(25, 40, 558)-net in base 16, using
- (u, u+v)-construction [i] based on
- (3, 10, 44)-net in base 16, using
- base change [i] based on digital (1, 8, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- base change [i] based on digital (1, 8, 44)-net over F32, using
- digital (15, 30, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 15, 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, 15, 257)-net over F256, using
- (3, 10, 44)-net in base 16, using
(40−15, 40, 1118)-Net over F16 — Digital
Digital (25, 40, 1118)-net over F16, using
(40−15, 40, 1152111)-Net in Base 16 — Upper bound on s
There is no (25, 40, 1152112)-net in base 16, because
- 1 times m-reduction [i] would yield (25, 39, 1152112)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 91344 062986 640924 575614 859899 529003 908579 069061 > 1639 [i]