MinT - Best Known (70−23, 70, s)-Nets in Base 5

Best Known (70−23, 70, s)-Nets in Base 5

(70−23, 70, 252)-Net over F₅ — Constructive and digital

Digital (47, 70, 252)-net over F₅, using

4 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]

(70−23, 70, 390)-Net over F₅ — Digital

Digital (47, 70, 390)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−23, 70, 29736)-Net in Base 5 — Upper bound on s

There is no (47, 70, 29737)-net in base 5, because

1 times m-reduction [i] would yield (47, 69, 29737)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 694406 547146 844672 231967 344112 056956 735986 802429 > 5⁶⁹ [i]