MinT - Best Known (150−76, 150, s)-Nets in Base 9

Best Known (150−76, 150, s)-Nets in Base 9

(150−76, 150, 165)-Net over F₉ — Constructive and digital

Digital (74, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(150−76, 150, 261)-Net over F₉ — Digital

Digital (74, 150, 261)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−76, 150, 10953)-Net in Base 9 — Upper bound on s

There is no (74, 150, 10954)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137287 935547 748181 180850 978135 596812 271712 923961 982925 816770 358313 975988 276879 554471 462162 387423 787781 634815 233510 995625 689799 040081 061688 805921 > 9¹⁵⁰ [i]