MinT - Best Known (67, 67+77, s)-Nets in Base 9

Best Known (67, 67+77, s)-Nets in Base 9

(67, 67+77, 165)-Net over F₉ — Constructive and digital

Digital (67, 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]

(67, 67+77, 202)-Net over F₉ — Digital

Digital (67, 144, 202)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+77, 7299)-Net in Base 9 — Upper bound on s

There is no (67, 144, 7300)-net in base 9, because

1 times m-reduction [i] would yield (67, 143, 7300)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28681 170079 171804 554401 340702 576989 123787 667817 885566 662247 967568 989442 402950 773864 849908 251910 869525 951248 863344 483974 686191 029385 370177 > 9¹⁴³ [i]