MinT - Best Known (58, 114, s)-Nets in Base 3

Best Known (58, 114, s)-Nets in Base 3

(58, 114, 56)-Net over F₃ — Constructive and digital

Digital (58, 114, 56)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 43, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 71, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(58, 114, 66)-Net over F₃ — Digital

Digital (58, 114, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 114, 468)-Net in Base 3 — Upper bound on s

There is no (58, 114, 469)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 601835 742802 422400 446936 884629 097724 507094 058407 607665 > 3¹¹⁴ [i]