MinT - Best Known (54, 116, s)-Nets in Base 8

Best Known (54, 116, s)-Nets in Base 8

(54, 116, 110)-Net over F₈ — Constructive and digital

Digital (54, 116, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 40, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (14, 76, 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]

(54, 116, 150)-Net over F₈ — Digital

Digital (54, 116, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 116, 4229)-Net in Base 8 — Upper bound on s

There is no (54, 116, 4230)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 577 002576 513749 188656 845966 943276 403022 639760 755925 186188 923172 407256 569452 426799 556817 589194 875618 310848 > 8¹¹⁶ [i]