MinT - Best Known (68, 122, s)-Nets in Base 9

Best Known (68, 122, s)-Nets in Base 9

(68, 122, 344)-Net over F₉ — Constructive and digital

Digital (68, 122, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 61, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(68, 122, 395)-Net over F₉ — Digital

Digital (68, 122, 395)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 122, 27978)-Net in Base 9 — Upper bound on s

There is no (68, 122, 27979)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 682979 623012 495282 208924 505353 965725 273676 298002 782009 947904 830513 056858 798251 740645 137392 431025 703773 999976 508105 > 9¹²² [i]