MinT - Best Known (68, 68+36, s)-Nets in Base 9

Best Known (68, 68+36, s)-Nets in Base 9

(68, 68+36, 740)-Net over F₉ — Constructive and digital

Digital (68, 104, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 52, 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]

(68, 68+36, 1208)-Net over F₉ — Digital

Digital (68, 104, 1208)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+36, 307911)-Net in Base 9 — Upper bound on s

There is no (68, 104, 307912)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1742 732472 083227 891575 577877 872176 144073 802662 859814 437679 915753 061710 494617 915166 263943 842560 051585 > 9¹⁰⁴ [i]