MinT - Best Known (65, 65+71, s)-Nets in Base 9

Best Known (65, 65+71, s)-Nets in Base 9

(65, 65+71, 165)-Net over F₉ — Constructive and digital

Digital (65, 136, 165)-net over F₉, using

t-expansion [i] based on digital (64, 136, 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, 65+71, 212)-Net over F₉ — Digital

Digital (65, 136, 212)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+71, 8312)-Net in Base 9 — Upper bound on s

There is no (65, 136, 8313)-net in base 9, because

1 times m-reduction [i] would yield (65, 135, 8313)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 667 488463 756351 123127 661727 587538 241144 677395 912210 025811 271839 404274 319518 692923 169293 681744 961340 321127 457825 947449 868237 447705 > 9¹³⁵ [i]