MinT - Best Known (134−42, 134, s)-Nets in Base 9

Best Known (134−42, 134, s)-Nets in Base 9

(134−42, 134, 740)-Net over F₉ — Constructive and digital

Digital (92, 134, 740)-net over F₉, using

t-expansion [i] based on digital (91, 134, 740)-net over F₉, using
- 16 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]

(134−42, 134, 2672)-Net over F₉ — Digital

Digital (92, 134, 2672)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−42, 134, 1331602)-Net in Base 9 — Upper bound on s

There is no (92, 134, 1331603)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 875825 501779 056016 218653 318042 309473 650640 179134 170737 798862 798867 448078 990434 810941 085217 017818 960209 695949 963791 332084 438905 > 9¹³⁴ [i]