MinT - Best Known (25−13, 25, s)-Nets in Base 8

Best Known (25−13, 25, s)-Nets in Base 8

(25−13, 25, 65)-Net over F₈ — Constructive and digital

Digital (12, 25, 65)-net over F₈, using

base reduction for projective spaces (embedding PG(12,64) in PG(24,8)) for nets [i] based on digital (0, 13, 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]

(25−13, 25, 1748)-Net in Base 8 — Upper bound on s

There is no (12, 25, 1749)-net in base 8, because

1 times m-reduction [i] would yield (12, 24, 1749)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4731 383695 892086 693384 > 8²⁴ [i]