MinT - Best Known (71, 71+49, s)-Nets in Base 5

Best Known (71, 71+49, s)-Nets in Base 5

(71, 71+49, 252)-Net over F₅ — Constructive and digital

Digital (71, 120, 252)-net over F₅, using

2 times m-reduction [i] based on digital (71, 122, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 61, 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]

(71, 71+49, 7144)-Net in Base 5 — Upper bound on s

There is no (71, 120, 7145)-net in base 5, because

1 times m-reduction [i] would yield (71, 119, 7145)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150751 970137 076775 464957 463381 283091 195792 850334 504107 718554 466344 071571 280536 785825 > 5¹¹⁹ [i]