MinT - Best Known (146−122, 146, s)-Nets in Base 9

Best Known (146−122, 146, s)-Nets in Base 9

(146−122, 146, 78)-Net over F₉ — Constructive and digital

Digital (24, 146, 78)-net over F₉, using

t-expansion [i] based on digital (22, 146, 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]

(146−122, 146, 92)-Net over F₉ — Digital

Digital (24, 146, 92)-net over F₉, using

t-expansion [i] based on digital (23, 146, 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]

(146−122, 146, 529)-Net in Base 9 — Upper bound on s

There is no (24, 146, 530)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22 265747 575573 214728 676721 988215 891204 315664 577961 850392 197912 914539 408869 059016 180851 099538 846264 542763 827203 826472 575739 224333 527893 142225 > 9¹⁴⁶ [i]