MinT - Best Known (57, 57+47, s)-Nets in Base 8

Best Known (57, 57+47, s)-Nets in Base 8

(57, 57+47, 256)-Net over F₈ — Constructive and digital

Digital (57, 104, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 52, 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]

(57, 57+47, 273)-Net over F₈ — Digital

Digital (57, 104, 273)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+47, 14900)-Net in Base 8 — Upper bound on s

There is no (57, 104, 14901)-net in base 8, because

1 times m-reduction [i] would yield (57, 103, 14901)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1042 999072 912005 333983 472513 708566 738469 696880 733662 450175 462136 585768 061919 008315 290340 186272 > 8¹⁰³ [i]