MinT - Best Known (73−55, 73, s)-Nets in Base 8

Best Known (73−55, 73, s)-Nets in Base 8

(73−55, 73, 65)-Net over F₈ — Constructive and digital

Digital (18, 73, 65)-net over F₈, using

t-expansion [i] based on digital (14, 73, 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]

(73−55, 73, 382)-Net in Base 8 — Upper bound on s

There is no (18, 73, 383)-net in base 8, because

1 times m-reduction [i] would yield (18, 72, 383)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 106113 731510 453650 162855 702498 050872 440955 321729 299729 134718 137316 > 8⁷² [i]