MinT - Best Known (112−51, 112, s)-Nets in Base 5

Best Known (112−51, 112, s)-Nets in Base 5

(112−51, 112, 132)-Net over F₅ — Constructive and digital

Digital (61, 112, 132)-net over F₅, using

2 times m-reduction [i] based on digital (61, 114, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 57, 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]

(112−51, 112, 157)-Net over F₅ — Digital

Digital (61, 112, 157)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−51, 112, 3210)-Net in Base 5 — Upper bound on s

There is no (61, 112, 3211)-net in base 5, because

1 times m-reduction [i] would yield (61, 111, 3211)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 387499 792596 703867 293852 296198 251628 561076 146999 086167 996663 118616 458963 263437 > 5¹¹¹ [i]