MinT - Best Known (124−46, 124, s)-Nets in Base 9

Best Known (124−46, 124, s)-Nets in Base 9

(124−46, 124, 740)-Net over F₉ — Constructive and digital

Digital (78, 124, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 62, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(124−46, 124, 961)-Net over F₉ — Digital

Digital (78, 124, 961)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−46, 124, 164414)-Net in Base 9 — Upper bound on s

There is no (78, 124, 164415)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21187 085330 886937 199732 640066 461174 673466 550287 248934 562092 493706 873095 422226 258372 086068 935105 797781 034844 758985 618761 > 9¹²⁴ [i]