MinT - Best Known (60, 60+41, s)-Nets in Base 8

Best Known (60, 60+41, s)-Nets in Base 8

(60, 60+41, 354)-Net over F₈ — Constructive and digital

Digital (60, 101, 354)-net over F₈, using

5 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 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]

(60, 60+41, 435)-Net over F₈ — Digital

Digital (60, 101, 435)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+41, 38861)-Net in Base 8 — Upper bound on s

There is no (60, 101, 38862)-net in base 8, because

1 times m-reduction [i] would yield (60, 100, 38862)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 037512 654570 905112 066609 976271 814028 752436 892801 608727 099853 094147 083969 270709 620413 012564 > 8¹⁰⁰ [i]