MinT - Best Known (102−77, 102, s)-Nets in Base 9

Best Known (102−77, 102, s)-Nets in Base 9

(102−77, 102, 78)-Net over F₉ — Constructive and digital

Digital (25, 102, 78)-net over F₉, using

t-expansion [i] based on digital (22, 102, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(102−77, 102, 96)-Net over F₉ — Digital

Digital (25, 102, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(102−77, 102, 622)-Net in Base 9 — Upper bound on s

There is no (25, 102, 623)-net in base 9, because

1 times m-reduction [i] would yield (25, 101, 623)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 442993 191924 632409 644994 455082 556217 032753 171445 494856 038343 205855 873339 029852 243354 949784 146385 > 9¹⁰¹ [i]