MinT - Best Known (136−43, 136, s)-Nets in Base 9

Best Known (136−43, 136, s)-Nets in Base 9

(136−43, 136, 740)-Net over F₉ — Constructive and digital

Digital (93, 136, 740)-net over F₉, using

t-expansion [i] based on digital (91, 136, 740)-net over F₉, using
- 14 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(136−43, 136, 2560)-Net over F₉ — Digital

Digital (93, 136, 2560)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−43, 136, 1478478)-Net in Base 9 — Upper bound on s

There is no (93, 136, 1478479)-net in base 9, because

1 times m-reduction [i] would yield (93, 135, 1478479)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 664 878147 816075 749423 507021 150449 080457 429373 686803 179338 171868 875582 188288 814509 288566 257340 293133 895258 730324 613281 477621 757913 > 9¹³⁵ [i]