MinT - Best Known (12, 12+63, s)-Nets in Base 81

Best Known (12, 12+63, s)-Nets in Base 81

(12, 12+63, 172)-Net over F₈₁ — Constructive and digital

Digital (12, 75, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 75, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(12, 12+63, 298)-Net over F₈₁ — Digital

Digital (12, 75, 298)-net over F₈₁, using

net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
  - a curve from the manYPoints database [i]

(12, 12+63, 5565)-Net in Base 81 — Upper bound on s

There is no (12, 75, 5566)-net in base 81, because

1 times m-reduction [i] would yield (12, 74, 5566)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1697 287604 358455 443831 822246 685280 315310 900702 886555 666799 325590 766099 556511 200330 622419 095051 943748 448211 558047 130826 193967 049923 229482 379681 > 81⁷⁴ [i]