Best Known (44, 44+25, s)-Nets in Base 16
(44, 44+25, 579)-Net over F16 — Constructive and digital
Digital (44, 69, 579)-net over F16, using
- 161 times duplication [i] based on digital (43, 68, 579)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 18, 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 (25, 50, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 25, 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, 25, 257)-net over F256, using
- digital (6, 18, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(44, 44+25, 1905)-Net over F16 — Digital
Digital (44, 69, 1905)-net over F16, using
(44, 44+25, 2347553)-Net in Base 16 — Upper bound on s
There is no (44, 69, 2347554)-net in base 16, because
- 1 times m-reduction [i] would yield (44, 68, 2347554)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 7588 557378 634349 645172 525064 297576 539645 391873 121484 673989 685413 589262 246063 965096 > 1668 [i]