Best Known (109−56, 109, s)-Nets in Base 16
(109−56, 109, 243)-Net over F16 — Constructive and digital
Digital (53, 109, 243)-net over F16, using
- t-expansion [i] based on digital (48, 109, 243)-net over F16, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
(109−56, 109, 336)-Net over F16 — Digital
Digital (53, 109, 336)-net over F16, using
(109−56, 109, 36660)-Net in Base 16 — Upper bound on s
There is no (53, 109, 36661)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 177513 120248 408885 708453 839978 475333 374436 869745 778969 618174 799476 376843 853041 282277 416719 588520 179662 146649 416264 831871 066163 921796 > 16109 [i]