Best Known (53, 125, s)-Nets in Base 16
(53, 125, 243)-Net over F16 — Constructive and digital
Digital (53, 125, 243)-net over F16, using
- t-expansion [i] based on digital (48, 125, 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
(53, 125, 255)-Net over F16 — Digital
Digital (53, 125, 255)-net over F16, using
- t-expansion [i] based on digital (50, 125, 255)-net over F16, using
- net from sequence [i] based on digital (50, 254)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 50 and N(F) ≥ 255, using
- net from sequence [i] based on digital (50, 254)-sequence over F16, using
(53, 125, 257)-Net in Base 16
(53, 125, 257)-net in base 16, using
- base change [i] based on digital (28, 100, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
(53, 125, 14421)-Net in Base 16 — Upper bound on s
There is no (53, 125, 14422)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 3 275056 391343 745235 872212 531020 499850 094290 286949 459752 087643 153760 216854 116267 734089 288594 463872 478519 667099 848829 636241 430450 354069 275954 738634 037506 > 16125 [i]