MinT - Best Known (65, 138, s)-Nets in Base 9

Best Known (65, 138, s)-Nets in Base 9

(65, 138, 165)-Net over F₉ — Constructive and digital

Digital (65, 138, 165)-net over F₉, using

t-expansion [i] based on digital (64, 138, 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, 138, 203)-Net over F₉ — Digital

Digital (65, 138, 203)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 138, 7617)-Net in Base 9 — Upper bound on s

There is no (65, 138, 7618)-net in base 9, because

1 times m-reduction [i] would yield (65, 137, 7618)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53954 435335 114860 769022 836756 707183 582288 508103 519562 822879 415612 519133 675185 784784 239023 005589 820426 088289 594509 287546 302522 675905 > 9¹³⁷ [i]