MinT - Best Known (66, 122, s)-Nets in Base 8

Best Known (66, 122, s)-Nets in Base 8

(66, 122, 256)-Net over F₈ — Constructive and digital

Digital (66, 122, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 61, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(66, 122, 292)-Net over F₈ — Digital

Digital (66, 122, 292)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 122, 13875)-Net in Base 8 — Upper bound on s

There is no (66, 122, 13876)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 150 426721 228835 679429 039496 695961 176944 968327 077311 573327 356331 580007 550879 955739 716858 122185 987684 991959 882936 > 8¹²² [i]