MinT - Best Known (143−42, 143, s)-Nets in Base 5

Best Known (143−42, 143, s)-Nets in Base 5

(143−42, 143, 400)-Net over F₅ — Constructive and digital

Digital (101, 143, 400)-net over F₅, using

t-expansion [i] based on digital (100, 143, 400)-net over F₅, using
- 7 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
  - trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(143−42, 143, 1126)-Net over F₅ — Digital

Digital (101, 143, 1126)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−42, 143, 124747)-Net in Base 5 — Upper bound on s

There is no (101, 143, 124748)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8968 836824 883854 332880 736408 161821 038477 544629 221120 176576 903262 252651 370241 932691 198670 805831 222193 > 5¹⁴³ [i]