MinT - Best Known (57, 57+55, s)-Nets in Base 8

Best Known (57, 57+55, s)-Nets in Base 8

(57, 57+55, 160)-Net over F₈ — Constructive and digital

Digital (57, 112, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 56, 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]

(57, 57+55, 206)-Net over F₈ — Digital

Digital (57, 112, 206)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+55, 8037)-Net in Base 8 — Upper bound on s

There is no (57, 112, 8038)-net in base 8, because

1 times m-reduction [i] would yield (57, 111, 8038)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17547 296248 944222 344246 653760 106665 149549 313768 385826 430634 732971 219904 249784 001770 101572 429688 417560 > 8¹¹¹ [i]