MinT - Best Known (49, 72, s)-Nets in Base 9

Best Known (49, 72, s)-Nets in Base 9

(49, 72, 448)-Net over F₉ — Constructive and digital

Digital (49, 72, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 36, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(49, 72, 1513)-Net over F₉ — Digital

Digital (49, 72, 1513)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 72, 885365)-Net in Base 9 — Upper bound on s

There is no (49, 72, 885366)-net in base 9, because

1 times m-reduction [i] would yield (49, 71, 885366)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 56 392296 093423 883431 811509 478782 065902 497378 715747 264808 215454 171985 > 9⁷¹ [i]