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

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

(43, 43+43, 130)-Net over F₈ — Constructive and digital

Digital (43, 86, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 43, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(43, 43+43, 155)-Net over F₈ — Digital

Digital (43, 86, 155)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+43, 5594)-Net in Base 8 — Upper bound on s

There is no (43, 86, 5595)-net in base 8, because

1 times m-reduction [i] would yield (43, 85, 5595)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 58032 033378 319400 354173 386692 718896 634898 105629 090915 206465 016508 449878 631468 > 8⁸⁵ [i]