MinT - Best Known (76, 76+63, s)-Nets in Base 9

Best Known (76, 76+63, s)-Nets in Base 9

(76, 76+63, 320)-Net over F₉ — Constructive and digital

Digital (76, 139, 320)-net over F₉, using

3 times m-reduction [i] based on digital (76, 142, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 71, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(76, 76+63, 396)-Net over F₉ — Digital

Digital (76, 139, 396)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+63, 27451)-Net in Base 9 — Upper bound on s

There is no (76, 139, 27452)-net in base 9, because

1 times m-reduction [i] would yield (76, 138, 27452)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485079 837738 998389 066365 785571 411142 345027 139782 621736 258349 042037 515364 062485 728919 041252 068373 490405 853028 493184 647302 458055 383969 > 9¹³⁸ [i]