MinT - Best Known (63, 63+30, s)-Nets in Base 9

Best Known (63, 63+30, s)-Nets in Base 9

(63, 63+30, 740)-Net over F₉ — Constructive and digital

Digital (63, 93, 740)-net over F₉, using

1 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+30, 1690)-Net over F₉ — Digital

Digital (63, 93, 1690)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+30, 662177)-Net in Base 9 — Upper bound on s

There is no (63, 93, 662178)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55533 969917 180752 862310 937623 100378 231015 146752 234238 835159 800631 227919 033035 991438 137009 > 9⁹³ [i]