Best Known (36−24, 36, s)-Nets in Base 81
(36−24, 36, 172)-Net over F81 — Constructive and digital
Digital (12, 36, 172)-net over F81, using
- t-expansion [i] based on digital (7, 36, 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
(36−24, 36, 298)-Net over F81 — Digital
Digital (12, 36, 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
(36−24, 36, 35128)-Net in Base 81 — Upper bound on s
There is no (12, 36, 35129)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 507 657059 952475 738027 179027 430463 727428 034853 778147 889896 863485 947841 > 8136 [i]