MinT - Best Known (63, 63+29, s)-Nets in Base 9

Best Known (63, 63+29, s)-Nets in Base 9

(63, 63+29, 740)-Net over F₉ — Constructive and digital

Digital (63, 92, 740)-net over F₉, using

2 times m-reduction [i] based on digital (63, 94, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 47, 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]

(63, 63+29, 1943)-Net over F₉ — Digital

Digital (63, 92, 1943)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+29, 1204872)-Net in Base 9 — Upper bound on s

There is no (63, 92, 1204873)-net in base 9, because

1 times m-reduction [i] would yield (63, 91, 1204873)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 600160 742036 436865 203912 423315 440461 085407 357239 218357 188115 461280 507855 046132 372401 > 9⁹¹ [i]