MinT - Best Known (13, 27, s)-Nets in Base 8

Best Known (13, 27, s)-Nets in Base 8

(13, 27, 65)-Net over F₈ — Constructive and digital

Digital (13, 27, 65)-net over F₈, using

base reduction for projective spaces (embedding PG(13,64) in PG(26,8)) for nets [i] based on digital (0, 14, 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]

(13, 27, 1465)-Net in Base 8 — Upper bound on s

There is no (13, 27, 1466)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 423647 506934 957989 482196 > 8²⁷ [i]