MinT - Best Known (91, 91+49, s)-Nets in Base 9

Best Known (91, 91+49, s)-Nets in Base 9

(91, 91+49, 740)-Net over F₉ — Constructive and digital

Digital (91, 140, 740)-net over F₉, using

10 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 75, 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]

(91, 91+49, 1446)-Net over F₉ — Digital

Digital (91, 140, 1446)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+49, 412014)-Net in Base 9 — Upper bound on s

There is no (91, 140, 412015)-net in base 9, because

1 times m-reduction [i] would yield (91, 139, 412015)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362480 349730 893182 279206 524580 551942 273975 253191 547529 865688 572397 717384 728145 014864 637159 420600 740556 865190 743117 036055 735371 103041 > 9¹³⁹ [i]