MinT - Best Known (65, 65+75, s)-Nets in Base 9

Best Known (65, 65+75, s)-Nets in Base 9

(65, 65+75, 165)-Net over F₉ — Constructive and digital

Digital (65, 140, 165)-net over F₉, using

t-expansion [i] based on digital (64, 140, 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+75, 195)-Net over F₉ — Digital

Digital (65, 140, 195)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+75, 7019)-Net in Base 9 — Upper bound on s

There is no (65, 140, 7020)-net in base 9, because

1 times m-reduction [i] would yield (65, 139, 7020)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 382508 511262 669247 656477 814098 840955 588704 546061 625045 145439 330056 467885 554293 749287 979560 129765 499740 787587 313411 896323 564053 702625 > 9¹³⁹ [i]