MinT - Best Known (23−12, 23, s)-Nets in Base 8

Best Known (23−12, 23, s)-Nets in Base 8

(23−12, 23, 65)-Net over F₈ — Constructive and digital

Digital (11, 23, 65)-net over F₈, using

base reduction for projective spaces (embedding PG(11,64) in PG(22,8)) for nets [i] based on digital (0, 12, 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]

(23−12, 23, 1235)-Net in Base 8 — Upper bound on s

There is no (11, 23, 1236)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 592 144862 203308 841036 > 8²³ [i]