MinT - Best Known (40−20, 40, s)-Nets in Base 8

Best Known (40−20, 40, s)-Nets in Base 8

(40−20, 40, 130)-Net over F₈ — Constructive and digital

Digital (20, 40, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 20, 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]

(40−20, 40, 2644)-Net in Base 8 — Upper bound on s

There is no (20, 40, 2645)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 334106 631255 306865 508480 678803 096772 > 8⁴⁰ [i]