MinT - Best Known (18, 65, s)-Nets in Base 8

Best Known (18, 65, s)-Nets in Base 8

(18, 65, 65)-Net over F₈ — Constructive and digital

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

t-expansion [i] based on digital (14, 65, 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]

(18, 65, 424)-Net in Base 8 — Upper bound on s

There is no (18, 65, 425)-net in base 8, because

1 times m-reduction [i] would yield (18, 64, 425)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6378 337238 299874 932431 457358 174331 894227 436497 075538 258256 > 8⁶⁴ [i]