MinT - Best Known (70, 70+41, s)-Nets in Base 5

Best Known (70, 70+41, s)-Nets in Base 5

(70, 70+41, 252)-Net over F₅ — Constructive and digital

Digital (70, 111, 252)-net over F₅, using

9 times m-reduction [i] based on digital (70, 120, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 60, 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, 70+41, 338)-Net over F₅ — Digital

Digital (70, 111, 338)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+41, 14492)-Net in Base 5 — Upper bound on s

There is no (70, 111, 14493)-net in base 5, because

1 times m-reduction [i] would yield (70, 110, 14493)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77076 797108 700048 915191 514798 379996 532833 485126 003741 482223 909667 378071 171505 > 5¹¹⁰ [i]