MinT - Best Known (109−86, 109, s)-Nets in Base 9

Best Known (109−86, 109, s)-Nets in Base 9

(109−86, 109, 78)-Net over F₉ — Constructive and digital

Digital (23, 109, 78)-net over F₉, using

t-expansion [i] based on digital (22, 109, 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]

(109−86, 109, 92)-Net over F₉ — Digital

Digital (23, 109, 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]

(109−86, 109, 527)-Net in Base 9 — Upper bound on s

There is no (23, 109, 528)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 105 463138 773518 648833 674869 710659 813214 172772 923124 295745 718150 601991 121621 869743 173067 186598 687802 053505 > 9¹⁰⁹ [i]