MinT - Best Known (63, 63+51, s)-Nets in Base 5

Best Known (63, 63+51, s)-Nets in Base 5

(63, 63+51, 132)-Net over F₅ — Constructive and digital

Digital (63, 114, 132)-net over F₅, using

4 times m-reduction [i] based on digital (63, 118, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 59, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(63, 63+51, 170)-Net over F₅ — Digital

Digital (63, 114, 170)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+51, 3653)-Net in Base 5 — Upper bound on s

There is no (63, 114, 3654)-net in base 5, because

1 times m-reduction [i] would yield (63, 113, 3654)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 639708 760924 345787 176966 860505 707051 272583 223077 486796 541346 925617 891858 434329 > 5¹¹³ [i]