MinT - Best Known (83, 134, s)-Nets in Base 9

Best Known (83, 134, s)-Nets in Base 9

(83, 134, 740)-Net over F₉ — Constructive and digital

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, 134, 903)-Net over F₉ — Digital

Digital (83, 134, 903)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 134, 151726)-Net in Base 9 — Upper bound on s

There is no (83, 134, 151727)-net in base 9, because

1 times m-reduction [i] would yield (83, 133, 151727)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 208390 419518 546203 185822 145764 707777 812302 750899 582125 751884 428369 504724 697695 755781 728807 884714 817457 877153 129238 910950 342841 > 9¹³³ [i]