MinT - Best Known (15, 58, s)-Nets in Base 8

Best Known (15, 58, s)-Nets in Base 8

(15, 58, 65)-Net over F₈ — Constructive and digital

Digital (15, 58, 65)-net over F₈, using

t-expansion [i] based on digital (14, 58, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(15, 58, 337)-Net in Base 8 — Upper bound on s

There is no (15, 58, 338)-net in base 8, because

1 times m-reduction [i] would yield (15, 57, 338)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3064 247301 760309 064250 017531 516510 749784 149755 733008 > 8⁵⁷ [i]