Best Known (53, 119, s)-Nets in Base 16
(53, 119, 243)-Net over F16 — Constructive and digital
Digital (53, 119, 243)-net over F16, using
- t-expansion [i] based on digital (48, 119, 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, 119, 255)-Net over F16 — Digital
Digital (53, 119, 255)-net over F16, using
- t-expansion [i] based on digital (50, 119, 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, 119, 257)-Net in Base 16
(53, 119, 257)-net in base 16, using
- 6 times m-reduction [i] based on (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
- base change [i] based on digital (28, 100, 257)-net over F32, using
(53, 119, 19274)-Net in Base 16 — Upper bound on s
There is no (53, 119, 19275)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 195282 561018 618509 124795 661040 876380 796914 064440 324275 917857 337982 701851 324772 808283 134589 572141 994444 765880 558723 172831 017670 809132 249791 519876 > 16119 [i]