MinT - Best Known (59, 59+43, s)-Nets in Base 8

Best Known (59, 59+43, s)-Nets in Base 8

(59, 59+43, 354)-Net over F₈ — Constructive and digital

Digital (59, 102, 354)-net over F₈, using

2 times m-reduction [i] based on digital (59, 104, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 52, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(59, 59+43, 366)-Net over F₈ — Digital

Digital (59, 102, 366)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+43, 27328)-Net in Base 8 — Upper bound on s

There is no (59, 102, 27329)-net in base 8, because

1 times m-reduction [i] would yield (59, 101, 27329)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 298594 135626 129792 663416 692709 259489 992305 799963 631767 659606 910933 935922 461054 310445 070784 > 8¹⁰¹ [i]