MinT - Best Known (36, 110, s)-Nets in Base 8

Best Known (36, 110, s)-Nets in Base 8

(36, 110, 65)-Net over F₈ — Constructive and digital

Digital (36, 110, 65)-net over F₈, using

t-expansion [i] based on digital (14, 110, 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]

(36, 110, 112)-Net over F₈ — Digital

Digital (36, 110, 112)-net over F₈, using

t-expansion [i] based on digital (35, 110, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(36, 110, 990)-Net in Base 8 — Upper bound on s

There is no (36, 110, 991)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2265 986676 808158 057258 152065 367185 874091 361694 958941 397927 877661 613154 886711 381010 046257 092382 162388 > 8¹¹⁰ [i]