MinT - Best Known (86−62, 86, s)-Nets in Base 9

Best Known (86−62, 86, s)-Nets in Base 9

(86−62, 86, 78)-Net over F₉ — Constructive and digital

Digital (24, 86, 78)-net over F₉, using

t-expansion [i] based on digital (22, 86, 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]

(86−62, 86, 92)-Net over F₉ — Digital

Digital (24, 86, 92)-net over F₉, using

t-expansion [i] based on digital (23, 86, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(86−62, 86, 670)-Net in Base 9 — Upper bound on s

There is no (24, 86, 671)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 12014 337167 093300 370443 131152 527273 939867 742022 705087 605499 279817 878459 638216 513033 > 9⁸⁶ [i]