MinT - Best Known (118−39, 118, s)-Nets in Base 9

Best Known (118−39, 118, s)-Nets in Base 9

(118−39, 118, 740)-Net over F₉ — Constructive and digital

Digital (79, 118, 740)-net over F₉, using

8 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 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]

(118−39, 118, 1744)-Net over F₉ — Digital

Digital (79, 118, 1744)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−39, 118, 745150)-Net in Base 9 — Upper bound on s

There is no (79, 118, 745151)-net in base 9, because

1 times m-reduction [i] would yield (79, 117, 745151)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4429 784277 640461 242527 613191 821613 194519 727616 616823 277343 514555 496856 548805 967474 043456 756946 614737 311223 298409 > 9¹¹⁷ [i]