MinT - Best Known (140−52, 140, s)-Nets in Base 9

Best Known (140−52, 140, s)-Nets in Base 9

(140−52, 140, 740)-Net over F₉ — Constructive and digital

Digital (88, 140, 740)-net over F₉, using

4 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 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]

(140−52, 140, 1059)-Net over F₉ — Digital

Digital (88, 140, 1059)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−52, 140, 181298)-Net in Base 9 — Upper bound on s

There is no (88, 140, 181299)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 262878 179282 080814 023177 053061 641500 891851 096671 250087 208566 444556 902575 773799 201379 449130 000350 735984 783472 019459 822453 048018 240241 > 9¹⁴⁰ [i]