MinT - Best Known (117−53, 117, s)-Nets in Base 5

Best Known (117−53, 117, s)-Nets in Base 5

(117−53, 117, 132)-Net over F₅ — Constructive and digital

Digital (64, 117, 132)-net over F₅, using

3 times m-reduction [i] based on digital (64, 120, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 60, 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]

(117−53, 117, 166)-Net over F₅ — Digital

Digital (64, 117, 166)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−53, 117, 3446)-Net in Base 5 — Upper bound on s

There is no (64, 117, 3447)-net in base 5, because

1 times m-reduction [i] would yield (64, 116, 3447)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1211 606777 077166 127407 179245 800018 077625 768950 285237 212975 101592 682768 109047 464857 > 5¹¹⁶ [i]