MinT - Best Known (51−34, 51, s)-Nets in Base 8

Best Known (51−34, 51, s)-Nets in Base 8

(51−34, 51, 65)-Net over F₈ — Constructive and digital

Digital (17, 51, 65)-net over F₈, using

t-expansion [i] based on digital (14, 51, 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]

(51−34, 51, 514)-Net in Base 8 — Upper bound on s

There is no (17, 51, 515)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11572 390390 770752 431859 341518 959228 622648 452416 > 8⁵¹ [i]