MinT - Best Known (140−51, 140, s)-Nets in Base 9

Best Known (140−51, 140, s)-Nets in Base 9

(140−51, 140, 740)-Net over F₉ — Constructive and digital

Digital (89, 140, 740)-net over F₉, using

6 times m-reduction [i] based on digital (89, 146, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 73, 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]

(140−51, 140, 1169)-Net over F₉ — Digital

Digital (89, 140, 1169)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−51, 140, 257097)-Net in Base 9 — Upper bound on s

There is no (89, 140, 257098)-net in base 9, because

1 times m-reduction [i] would yield (89, 139, 257098)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362246 038506 751698 921506 679413 414732 791153 732781 371847 973336 061743 635129 778711 793772 244588 625620 493961 836313 153628 113227 012357 461713 > 9¹³⁹ [i]