MinT - Best Known (69, 144, s)-Nets in Base 9

Best Known (69, 144, s)-Nets in Base 9

(69, 144, 165)-Net over F₉ — Constructive and digital

Digital (69, 144, 165)-net over F₉, using

t-expansion [i] based on digital (64, 144, 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]

(69, 144, 225)-Net over F₉ — Digital

Digital (69, 144, 225)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 144, 8907)-Net in Base 9 — Upper bound on s

There is no (69, 144, 8908)-net in base 9, because

1 times m-reduction [i] would yield (69, 143, 8908)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28720 427822 441560 846519 495624 504962 745911 907316 684966 530427 426109 414942 084671 641005 302585 281707 198448 036604 196754 502704 702624 606831 142625 > 9¹⁴³ [i]