MinT - Best Known (143−43, 143, s)-Nets in Base 5

Best Known (143−43, 143, s)-Nets in Base 5

(143−43, 143, 400)-Net over F₅ — Constructive and digital

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]

(143−43, 143, 1011)-Net over F₅ — Digital

Digital (100, 143, 1011)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−43, 143, 115543)-Net in Base 5 — Upper bound on s

There is no (100, 143, 115544)-net in base 5, because

1 times m-reduction [i] would yield (100, 142, 115544)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1793 968669 639178 299436 996781 598532 207497 527732 248757 145053 604171 227806 133619 722915 826097 263390 138465 > 5¹⁴² [i]