MinT - Best Known (88, 130, s)-Nets in Base 9

Best Known (88, 130, s)-Nets in Base 9

(88, 130, 740)-Net over F₉ — Constructive and digital

Digital (88, 130, 740)-net over F₉, using

14 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 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]

(88, 130, 2161)-Net over F₉ — Digital

Digital (88, 130, 2161)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 130, 876217)-Net in Base 9 — Upper bound on s

There is no (88, 130, 876218)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11259 855159 784750 857055 938520 162973 612034 175031 206148 003293 124902 219886 136036 434570 514711 767547 238420 623246 284666 610221 600145 > 9¹³⁰ [i]