MinT - Best Known (63, 123, s)-Nets in Base 5

Best Known (63, 123, s)-Nets in Base 5

(63, 123, 84)-Net over F₅ — Constructive and digital

Digital (63, 123, 84)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (2, 32, 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, 91, 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]

(63, 123, 134)-Net over F₅ — Digital

Digital (63, 123, 134)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 123, 2188)-Net in Base 5 — Upper bound on s

There is no (63, 123, 2189)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 480472 956549 291754 434586 221182 793917 239705 429800 505705 796957 921565 563779 552426 171689 > 5¹²³ [i]