Best Known (63−56, 63, s)-Nets in Base 81
(63−56, 63, 172)-Net over F81 — Constructive and digital
Digital (7, 63, 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
(63−56, 63, 190)-Net over F81 — Digital
Digital (7, 63, 190)-net over F81, using
- t-expansion [i] based on digital (6, 63, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(63−56, 63, 2765)-Net in Base 81 — Upper bound on s
There is no (7, 63, 2766)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 1 717584 487102 177281 823497 226235 052185 027857 648518 947726 380522 858066 091442 679836 393375 507086 591610 221645 825453 339992 999041 > 8163 [i]