Best Known (121−68, 121, s)-Nets in Base 16
(121−68, 121, 243)-Net over F16 — Constructive and digital
Digital (53, 121, 243)-net over F16, using
- t-expansion [i] based on digital (48, 121, 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
(121−68, 121, 255)-Net over F16 — Digital
Digital (53, 121, 255)-net over F16, using
- t-expansion [i] based on digital (50, 121, 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
(121−68, 121, 257)-Net in Base 16
(53, 121, 257)-net in base 16, using
- 4 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
(121−68, 121, 17384)-Net in Base 16 — Upper bound on s
There is no (53, 121, 17385)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 49 980947 392440 334047 243477 824056 975542 997909 173630 954599 712371 294272 632604 220316 074620 972450 766188 784041 732258 589344 394365 390854 384479 322598 997476 > 16121 [i]