MinT - Best Known (42−25, 42, s)-Nets in Base 8

Best Known (42−25, 42, s)-Nets in Base 8

(42−25, 42, 65)-Net over F₈ — Constructive and digital

Digital (17, 42, 65)-net over F₈, using

t-expansion [i] based on digital (14, 42, 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]

(42−25, 42, 912)-Net in Base 8 — Upper bound on s

There is no (17, 42, 913)-net in base 8, because

1 times m-reduction [i] would yield (17, 41, 913)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 651345 840927 308335 764061 848690 054524 > 8⁴¹ [i]