MinT - Best Known (85, 85+45, s)-Nets in Base 9

Best Known (85, 85+45, s)-Nets in Base 9

(85, 85+45, 740)-Net over F₉ — Constructive and digital

Digital (85, 130, 740)-net over F₉, using

8 times m-reduction [i] based on digital (85, 138, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 69, 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]

(85, 85+45, 1445)-Net over F₉ — Digital

Digital (85, 130, 1445)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+45, 445739)-Net in Base 9 — Upper bound on s

There is no (85, 130, 445740)-net in base 9, because

1 times m-reduction [i] would yield (85, 129, 445740)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 101433 604955 660290 036077 111430 558747 127293 696853 290394 274835 216069 388987 616707 598897 274010 233667 514234 553495 750098 784961 > 9¹²⁹ [i]