MinT - Best Known (116−57, 116, s)-Nets in Base 8

Best Known (116−57, 116, s)-Nets in Base 8

(116−57, 116, 160)-Net over F₈ — Constructive and digital

Digital (59, 116, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 58, 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]

(116−57, 116, 211)-Net over F₈ — Digital

Digital (59, 116, 211)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−57, 116, 8243)-Net in Base 8 — Upper bound on s

There is no (59, 116, 8244)-net in base 8, because

1 times m-reduction [i] would yield (59, 115, 8244)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 71 818595 270884 517815 590260 890985 618325 247712 783072 566860 184309 566589 424909 608529 059215 398191 649006 392120 > 8¹¹⁵ [i]