MinT - Best Known (72, 72+29, s)-Nets in Base 5

Best Known (72, 72+29, s)-Nets in Base 5

(72, 72+29, 296)-Net over F₅ — Constructive and digital

Digital (72, 101, 296)-net over F₅, using

5 times m-reduction [i] based on digital (72, 106, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 53, 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]

(72, 72+29, 952)-Net over F₅ — Digital

Digital (72, 101, 952)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+29, 148597)-Net in Base 5 — Upper bound on s

There is no (72, 101, 148598)-net in base 5, because

1 times m-reduction [i] would yield (72, 100, 148598)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7889 003847 508367 833097 654311 354495 498310 042635 106030 075430 034691 370945 > 5¹⁰⁰ [i]