MinT - Best Known (64, 96, s)-Nets in Base 9

Best Known (64, 96, s)-Nets in Base 9

(64, 96, 740)-Net over F₉ — Constructive and digital

Digital (64, 96, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 48, 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]

(64, 96, 1415)-Net over F₉ — Digital

Digital (64, 96, 1415)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 96, 451746)-Net in Base 9 — Upper bound on s

There is no (64, 96, 451747)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 484684 359169 995000 256259 543777 107958 219327 726790 373486 890050 614264 929149 491213 784779 236737 > 9⁹⁶ [i]