MinT - Best Known (59, 59+58, s)-Nets in Base 3

Best Known (59, 59+58, s)-Nets in Base 3

(59, 59+58, 56)-Net over F₃ — Constructive and digital

Digital (59, 117, 56)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 44, 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, 73, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃ (see above)

(59, 59+58, 66)-Net over F₃ — Digital

Digital (59, 117, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+58, 463)-Net in Base 3 — Upper bound on s

There is no (59, 117, 464)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 70 145043 554945 794520 040194 956781 859287 810867 830014 501537 > 3¹¹⁷ [i]