MinT - Best Known (60, 60+58, s)-Nets in Base 8

Best Known (60, 60+58, s)-Nets in Base 8

(60, 60+58, 160)-Net over F₈ — Constructive and digital

Digital (60, 118, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 59, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(60, 60+58, 214)-Net over F₈ — Digital

Digital (60, 118, 214)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+58, 7864)-Net in Base 8 — Upper bound on s

There is no (60, 118, 7865)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36776 156706 599971 544318 772012 098875 175318 553142 963139 040469 431716 687209 998949 918524 531516 258423 713954 516896 > 8¹¹⁸ [i]