MinT - Best Known (67, 67+67, s)-Nets in Base 9

Best Known (67, 67+67, s)-Nets in Base 9

(67, 67+67, 165)-Net over F₉ — Constructive and digital

Digital (67, 134, 165)-net over F₉, using

t-expansion [i] based on digital (64, 134, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(67, 67+67, 251)-Net over F₉ — Digital

Digital (67, 134, 251)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+67, 11518)-Net in Base 9 — Upper bound on s

There is no (67, 134, 11519)-net in base 9, because

1 times m-reduction [i] would yield (67, 133, 11519)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 221972 013563 750731 909537 599442 551640 541093 782255 684126 628766 433603 188299 489717 906606 111712 406383 152365 373735 944131 606472 845049 > 9¹³³ [i]