MinT - Best Known (15−8, 15, s)-Nets in Base 8

Best Known (15−8, 15, s)-Nets in Base 8

(15−8, 15, 65)-Net over F₈ — Constructive and digital

Digital (7, 15, 65)-net over F₈, using

base reduction for projective spaces (embedding PG(7,64) in PG(14,8)) for nets [i] based on digital (0, 8, 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]

(15−8, 15, 768)-Net in Base 8 — Upper bound on s

There is no (7, 15, 769)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 35 363454 043968 > 8¹⁵ [i]