MinT - Best Known (106, 106+40, s)-Nets in Base 5

Best Known (106, 106+40, s)-Nets in Base 5

(106, 106+40, 408)-Net over F₅ — Constructive and digital

Digital (106, 146, 408)-net over F₅, using

t-expansion [i] based on digital (105, 146, 408)-net over F₅, using
- 4 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
  - trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
    - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
        a function field by GarcÃa and Quoos [i]

(106, 106+40, 1612)-Net over F₅ — Digital

Digital (106, 146, 1612)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+40, 262847)-Net in Base 5 — Upper bound on s

There is no (106, 146, 262848)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121109 106974 306738 555555 412317 647364 157915 631377 236608 047632 558105 167407 798005 312264 527133 734817 914881 > 5¹⁴⁶ [i]