MinT - Best Known (67, 67+27, s)-Nets in Base 9

Best Known (67, 67+27, s)-Nets in Base 9

(67, 67+27, 740)-Net over F₉ — Constructive and digital

Digital (67, 94, 740)-net over F₉, using

8 times m-reduction [i] based on digital (67, 102, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 51, 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]

(67, 67+27, 3730)-Net over F₉ — Digital

Digital (67, 94, 3730)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+27, 4751378)-Net in Base 9 — Upper bound on s

There is no (67, 94, 4751379)-net in base 9, because

1 times m-reduction [i] would yield (67, 93, 4751379)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55533 409146 038537 161384 355020 800300 940491 735520 363572 988456 578411 000234 271433 020706 834617 > 9⁹³ [i]