MinT - Best Known (66, 66+67, s)-Nets in Base 9

Best Known (66, 66+67, s)-Nets in Base 9

(66, 66+67, 165)-Net over F₉ — Constructive and digital

Digital (66, 133, 165)-net over F₉, using

t-expansion [i] based on digital (64, 133, 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]

(66, 66+67, 242)-Net over F₉ — Digital

Digital (66, 133, 242)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+67, 10775)-Net in Base 9 — Upper bound on s

There is no (66, 133, 10776)-net in base 9, because

1 times m-reduction [i] would yield (66, 132, 10776)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 914344 868311 665931 299262 924001 448996 552859 289664 226309 129689 353207 315475 464736 738565 955031 775102 803830 433345 317816 187685 443777 > 9¹³² [i]