MinT - Best Known (61, 120, s)-Nets in Base 8

Best Known (61, 120, s)-Nets in Base 8

(61, 120, 160)-Net over F₈ — Constructive and digital

Digital (61, 120, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 60, 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]

(61, 120, 217)-Net over F₈ — Digital

Digital (61, 120, 217)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 120, 8450)-Net in Base 8 — Upper bound on s

There is no (61, 120, 8451)-net in base 8, because

1 times m-reduction [i] would yield (61, 119, 8451)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 294192 007788 545567 351910 678381 305082 561494 400904 767302 865392 835197 818739 053277 826762 298974 104684 766368 814464 > 8¹¹⁹ [i]