MinT - Best Known (140−53, 140, s)-Nets in Base 9

Best Known (140−53, 140, s)-Nets in Base 9

(140−53, 140, 740)-Net over F₉ — Constructive and digital

Digital (87, 140, 740)-net over F₉, using

2 times m-reduction [i] based on digital (87, 142, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 71, 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]

(140−53, 140, 962)-Net over F₉ — Digital

Digital (87, 140, 962)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−53, 140, 166605)-Net in Base 9 — Upper bound on s

There is no (87, 140, 166606)-net in base 9, because

1 times m-reduction [i] would yield (87, 139, 166606)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362591 847175 183243 694284 440435 468525 626058 287064 566862 993198 504524 635580 349695 104011 717296 188347 372917 602488 323961 884049 803032 294049 > 9¹³⁹ [i]