Best Known (163, 224, s)-Nets in Base 4
(163, 224, 531)-Net over F4 — Constructive and digital
Digital (163, 224, 531)-net over F4, using
- 10 times m-reduction [i] based on digital (163, 234, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 78, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 78, 177)-net over F64, using
(163, 224, 1391)-Net over F4 — Digital
Digital (163, 224, 1391)-net over F4, using
(163, 224, 119919)-Net in Base 4 — Upper bound on s
There is no (163, 224, 119920)-net in base 4, because
- 1 times m-reduction [i] would yield (163, 223, 119920)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 181 713632 141445 599994 425026 838115 363863 018358 560150 358906 015824 022101 843687 342994 559226 097018 979466 664658 531623 272344 448908 866816 162946 > 4223 [i]