MinT - Best Known (124−95, 124, s)-Nets in Base 9

Best Known (124−95, 124, s)-Nets in Base 9

(124−95, 124, 78)-Net over F₉ — Constructive and digital

Digital (29, 124, 78)-net over F₉, using

t-expansion [i] based on digital (22, 124, 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]

(124−95, 124, 110)-Net over F₉ — Digital

Digital (29, 124, 110)-net over F₉, using

t-expansion [i] based on digital (26, 124, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(124−95, 124, 693)-Net in Base 9 — Upper bound on s

There is no (29, 124, 694)-net in base 9, because

1 times m-reduction [i] would yield (29, 123, 694)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2506 934923 701534 621498 476722 236797 998601 264551 843074 282259 370724 317079 292126 351336 179236 686973 504006 761810 202959 201425 > 9¹²³ [i]