MinT - Best Known (83, 83+37, s)-Nets in Base 9

Best Known (83, 83+37, s)-Nets in Base 9

(83, 83+37, 740)-Net over F₉ — Constructive and digital

Digital (83, 120, 740)-net over F₉, using

14 times m-reduction [i] based on digital (83, 134, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 67, 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]

(83, 83+37, 2725)-Net over F₉ — Digital

Digital (83, 120, 2725)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+37, 1921502)-Net in Base 9 — Upper bound on s

There is no (83, 120, 1921503)-net in base 9, because

1 times m-reduction [i] would yield (83, 119, 1921503)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 358807 641242 664748 014096 465877 139611 307422 585898 592596 276048 827140 442572 133271 953797 657582 759428 613610 272963 998065 > 9¹¹⁹ [i]