Best Known (64−50, 64, s)-Nets in Base 81
(64−50, 64, 224)-Net over F81 — Constructive and digital
Digital (14, 64, 224)-net over F81, using
- t-expansion [i] based on digital (13, 64, 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
(64−50, 64, 298)-Net over F81 — Digital
Digital (14, 64, 298)-net over F81, using
- t-expansion [i] based on digital (12, 64, 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
(64−50, 64, 9765)-Net in Base 81 — Upper bound on s
There is no (14, 64, 9766)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 139 058783 662559 823727 983168 411974 189866 231780 795823 722207 078480 422386 568574 799358 428191 330989 821201 997851 179801 529762 252001 > 8164 [i]