MinT - Best Known (54, 87, s)-Nets in Base 5

Best Known (54, 87, s)-Nets in Base 5

(54, 87, 252)-Net over F₅ — Constructive and digital

Digital (54, 87, 252)-net over F₅, using

1 times m-reduction [i] based on digital (54, 88, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 44, 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]

(54, 87, 9703)-Net in Base 5 — Upper bound on s

There is no (54, 87, 9704)-net in base 5, because

1 times m-reduction [i] would yield (54, 86, 9704)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 293538 098294 111956 086176 373354 110121 929218 715910 839170 852865 > 5⁸⁶ [i]