MinT - Best Known (62, 62+56, s)-Nets in Base 8

Best Known (62, 62+56, s)-Nets in Base 8

(62, 62+56, 208)-Net over F₈ — Constructive and digital

Digital (62, 118, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 59, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(62, 62+56, 248)-Net over F₈ — Digital

Digital (62, 118, 248)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+56, 10305)-Net in Base 8 — Upper bound on s

There is no (62, 118, 10306)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36791 583548 252563 332165 672691 107703 509727 740685 636520 368082 261590 800021 128061 034927 964049 658249 279518 674704 > 8¹¹⁸ [i]