MinT - Best Known (66, 66+73, s)-Nets in Base 9

Best Known (66, 66+73, s)-Nets in Base 9

(66, 66+73, 165)-Net over F₉ — Constructive and digital

Digital (66, 139, 165)-net over F₉, using

t-expansion [i] based on digital (64, 139, 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]

(66, 66+73, 211)-Net over F₉ — Digital

Digital (66, 139, 211)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+73, 8098)-Net in Base 9 — Upper bound on s

There is no (66, 139, 8099)-net in base 9, because

1 times m-reduction [i] would yield (66, 138, 8099)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485973 963927 010501 369199 966723 057541 556743 857211 840104 539150 869521 349172 801239 956229 115584 124657 752638 497153 001622 275531 437835 538529 > 9¹³⁸ [i]