MinT - Best Known (10, 10+11, s)-Nets in Base 8

Best Known (10, 10+11, s)-Nets in Base 8

(10, 10+11, 65)-Net over F₈ — Constructive and digital

Digital (10, 21, 65)-net over F₈, using

base reduction for projective spaces (embedding PG(10,64) in PG(20,8)) for nets [i] based on digital (0, 11, 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]

(10, 10+11, 1521)-Net in Base 8 — Upper bound on s

There is no (10, 21, 1522)-net in base 8, because

1 times m-reduction [i] would yield (10, 20, 1522)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 154114 356146 557996 > 8²⁰ [i]