MinT - Best Known (130−65, 130, s)-Nets in Base 9

Best Known (130−65, 130, s)-Nets in Base 9

(130−65, 130, 165)-Net over F₉ — Constructive and digital

Digital (65, 130, 165)-net over F₉, using

t-expansion [i] based on digital (64, 130, 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]

(130−65, 130, 245)-Net over F₉ — Digital

Digital (65, 130, 245)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−65, 130, 11215)-Net in Base 9 — Upper bound on s

There is no (65, 130, 11216)-net in base 9, because

1 times m-reduction [i] would yield (65, 129, 11216)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1252 138600 637703 866836 278763 109604 607759 439897 172028 539066 033312 902843 965683 512875 941004 423413 573506 948249 095421 820340 809729 > 9¹²⁹ [i]