MinT - Best Known (70, 70+44, s)-Nets in Base 5

Best Known (70, 70+44, s)-Nets in Base 5

(70, 70+44, 252)-Net over F₅ — Constructive and digital

Digital (70, 114, 252)-net over F₅, using

6 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+44, 290)-Net over F₅ — Digital

Digital (70, 114, 290)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+44, 9462)-Net in Base 5 — Upper bound on s

There is no (70, 114, 9463)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 230184 197933 167091 856990 925910 983405 834682 440014 619334 860715 554595 437991 860905 > 5¹¹⁴ [i]