MinT - Best Known (32, 116, s)-Nets in Base 8

Best Known (32, 116, s)-Nets in Base 8

(32, 116, 65)-Net over F₈ — Constructive and digital

Digital (32, 116, 65)-net over F₈, using

t-expansion [i] based on digital (14, 116, 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]

(32, 116, 97)-Net over F₈ — Digital

Digital (32, 116, 97)-net over F₈, using

t-expansion [i] based on digital (28, 116, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(32, 116, 709)-Net in Base 8 — Upper bound on s

There is no (32, 116, 710)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 576 235951 553405 761732 859662 691099 718778 962107 450525 640258 984558 699987 187281 025313 613692 219496 499231 982384 > 8¹¹⁶ [i]