MinT - Best Known (54−35, 54, s)-Nets in Base 8

Best Known (54−35, 54, s)-Nets in Base 8

(54−35, 54, 65)-Net over F₈ — Constructive and digital

Digital (19, 54, 65)-net over F₈, using

t-expansion [i] based on digital (14, 54, 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]

(54−35, 54, 660)-Net in Base 8 — Upper bound on s

There is no (19, 54, 661)-net in base 8, because

1 times m-reduction [i] would yield (19, 53, 661)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 748235 456560 625991 578119 971502 899877 876105 591284 > 8⁵³ [i]