MinT - Best Known (112−33, 112, s)-Nets in Base 5

Best Known (112−33, 112, s)-Nets in Base 5

(112−33, 112, 296)-Net over F₅ — Constructive and digital

Digital (79, 112, 296)-net over F₅, using

8 times m-reduction [i] based on digital (79, 120, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 60, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(112−33, 112, 910)-Net over F₅ — Digital

Digital (79, 112, 910)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−33, 112, 120099)-Net in Base 5 — Upper bound on s

There is no (79, 112, 120100)-net in base 5, because

1 times m-reduction [i] would yield (79, 111, 120100)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385206 577867 359693 951993 360674 933048 183370 446772 439519 243450 877429 764390 727681 > 5¹¹¹ [i]