MinT - Best Known (74−59, 74, s)-Nets in Base 81

Best Known (74−59, 74, s)-Nets in Base 81

(74−59, 74, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 74, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 74, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(74−59, 74, 298)-Net over F₈₁ — Digital

Digital (15, 74, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 74, 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]

(74−59, 74, 9278)-Net in Base 81 — Upper bound on s

There is no (15, 74, 9279)-net in base 81, because

1 times m-reduction [i] would yield (15, 73, 9279)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 896733 485534 943239 754698 245947 108705 954333 093721 043980 072178 500726 016196 685011 510360 540898 666412 412780 513074 696455 942861 248202 489453 591281 > 81⁷³ [i]