MinT - Best Known (18, 18+45, s)-Nets in Base 8

Best Known (18, 18+45, s)-Nets in Base 8

(18, 18+45, 65)-Net over F₈ — Constructive and digital

Digital (18, 63, 65)-net over F₈, using

t-expansion [i] based on digital (14, 63, 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, 18+45, 440)-Net in Base 8 — Upper bound on s

There is no (18, 63, 441)-net in base 8, because

1 times m-reduction [i] would yield (18, 62, 441)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 101 740969 736812 036129 413531 101678 628990 037805 988206 727292 > 8⁶² [i]