Best Known (12, 82, s)-Nets in Base 81
(12, 82, 172)-Net over F81 — Constructive and digital
Digital (12, 82, 172)-net over F81, using
- t-expansion [i] based on digital (7, 82, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(12, 82, 298)-Net over F81 — Digital
Digital (12, 82, 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
(12, 82, 5128)-Net in Base 81 — Upper bound on s
There is no (12, 82, 5129)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 137746 959649 315115 466210 297083 185853 457387 195607 575542 981582 059798 410789 105896 980701 450621 268179 210610 708803 040764 315674 263312 822236 699698 214099 683966 841201 > 8182 [i]