MinT - Best Known (88, 88+44, s)-Nets in Base 5

Best Known (88, 88+44, s)-Nets in Base 5

(88, 88+44, 296)-Net over F₅ — Constructive and digital

Digital (88, 132, 296)-net over F₅, using

6 times m-reduction [i] based on digital (88, 138, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 69, 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]

(88, 88+44, 599)-Net over F₅ — Digital

Digital (88, 132, 599)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+44, 35352)-Net in Base 5 — Upper bound on s

There is no (88, 132, 35353)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 761147 663009 789928 794089 734101 437252 790280 369722 319570 609201 465665 045247 541738 027421 663945 > 5¹³² [i]