Best Known (109−60, 109, s)-Nets in Base 16
(109−60, 109, 243)-Net over F16 — Constructive and digital
Digital (49, 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
(109−60, 109, 257)-Net in Base 16
(49, 109, 257)-net in base 16, using
- 2 times m-reduction [i] based on (49, 111, 257)-net in base 16, using
- base change [i] based on digital (12, 74, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 74, 257)-net over F64, using
(109−60, 109, 19023)-Net in Base 16 — Upper bound on s
There is no (49, 109, 19024)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 177592 941364 820144 659471 132160 625907 640673 802471 378375 433110 886068 369879 082065 205352 593444 906750 152117 550351 917712 854321 218189 657676 > 16109 [i]