MinT - Best Known (120−55, 120, s)-Nets in Base 5

Best Known (120−55, 120, s)-Nets in Base 5

(120−55, 120, 132)-Net over F₅ — Constructive and digital

Digital (65, 120, 132)-net over F₅, using

2 times m-reduction [i] based on digital (65, 122, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 61, 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]

(120−55, 120, 162)-Net over F₅ — Digital

Digital (65, 120, 162)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−55, 120, 3268)-Net in Base 5 — Upper bound on s

There is no (65, 120, 3269)-net in base 5, because

1 times m-reduction [i] would yield (65, 119, 3269)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150771 365618 967145 757263 480192 515534 553929 022910 697045 092709 412034 589205 219672 367085 > 5¹¹⁹ [i]