MinT - Best Known (18−9, 18, s)-Nets in Base 8

Best Known (18−9, 18, s)-Nets in Base 8

(18−9, 18, 130)-Net over F₈ — Constructive and digital

Digital (9, 18, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(18−9, 18, 2176)-Net in Base 8 — Upper bound on s

There is no (9, 18, 2177)-net in base 8, because

1 times m-reduction [i] would yield (9, 17, 2177)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2255 621351 627232 > 8¹⁷ [i]