Best Known (63−49, 63, s)-Nets in Base 81
(63−49, 63, 224)-Net over F81 — Constructive and digital
Digital (14, 63, 224)-net over F81, using
- t-expansion [i] based on digital (13, 63, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(63−49, 63, 298)-Net over F81 — Digital
Digital (14, 63, 298)-net over F81, using
- t-expansion [i] based on digital (12, 63, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(63−49, 63, 10424)-Net in Base 81 — Upper bound on s
There is no (14, 63, 10425)-net in base 81, because
- 1 times m-reduction [i] would yield (14, 62, 10425)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 21235 772269 993764 044530 083900 153761 593904 622530 284262 476367 869370 013737 396874 418879 114968 383977 979193 125374 682880 176001 > 8162 [i]