MinT - Best Known (120−58, 120, s)-Nets in Base 5

Best Known (120−58, 120, s)-Nets in Base 5

(120−58, 120, 84)-Net over F₅ — Constructive and digital

Digital (62, 120, 84)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (2, 31, 12)-net over F₅, using
  - net from sequence [i] based on digital (2, 11)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 2 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 89, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(120−58, 120, 136)-Net over F₅ — Digital

Digital (62, 120, 136)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−58, 120, 2255)-Net in Base 5 — Upper bound on s

There is no (62, 120, 2256)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 754605 904317 087297 964800 921587 221896 981044 969016 967167 926832 341174 803997 095754 543425 > 5¹²⁰ [i]