MinT - Best Known (65, 134, s)-Nets in Base 9

Best Known (65, 134, s)-Nets in Base 9

(65, 134, 165)-Net over F₉ — Constructive and digital

Digital (65, 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]

(65, 134, 222)-Net over F₉ — Digital

Digital (65, 134, 222)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 134, 9123)-Net in Base 9 — Upper bound on s

There is no (65, 134, 9124)-net in base 9, because

1 times m-reduction [i] would yield (65, 133, 9124)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 217032 623438 601952 305852 663089 990079 472178 920585 509033 941386 046155 481028 283038 404026 877443 558705 829285 230088 081458 661568 163009 > 9¹³³ [i]