MinT - Best Known (72−25, 72, s)-Nets in Base 5

Best Known (72−25, 72, s)-Nets in Base 5

(72−25, 72, 252)-Net over F₅ — Constructive and digital

Digital (47, 72, 252)-net over F₅, using

2 times m-reduction [i] based on digital (47, 74, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(72−25, 72, 318)-Net over F₅ — Digital

Digital (47, 72, 318)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−25, 72, 18057)-Net in Base 5 — Upper bound on s

There is no (47, 72, 18058)-net in base 5, because

1 times m-reduction [i] would yield (47, 71, 18058)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 42 351696 546985 636111 440875 278938 196529 549511 495105 > 5⁷¹ [i]