MinT - Best Known (41−21, 41, s)-Nets in Base 8

Best Known (41−21, 41, s)-Nets in Base 8

(41−21, 41, 65)-Net over F₈ — Constructive and digital

Digital (20, 41, 65)-net over F₈, using

t-expansion [i] based on digital (14, 41, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(41−21, 41, 83)-Net over F₈ — Digital

Digital (20, 41, 83)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−21, 41, 2644)-Net in Base 8 — Upper bound on s

There is no (20, 41, 2645)-net in base 8, because

1 times m-reduction [i] would yield (20, 40, 2645)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 334106 631255 306865 508480 678803 096772 > 8⁴⁰ [i]