MinT - Best Known (113−34, 113, s)-Nets in Base 9

Best Known (113−34, 113, s)-Nets in Base 9

(113−34, 113, 740)-Net over F₉ — Constructive and digital

Digital (79, 113, 740)-net over F₉, using

13 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 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]

(113−34, 113, 3063)-Net over F₉ — Digital

Digital (79, 113, 3063)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−34, 113, 1975873)-Net in Base 9 — Upper bound on s

There is no (79, 113, 1975874)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 675159 350823 117296 715054 836527 097314 904870 105665 414686 040326 919580 803048 617176 414982 469988 971365 989473 646865 > 9¹¹³ [i]