MinT - Best Known (71, 117, s)-Nets in Base 5

Best Known (71, 117, s)-Nets in Base 5

(71, 117, 252)-Net over F₅ — Constructive and digital

Digital (71, 117, 252)-net over F₅, using

5 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, 117, 276)-Net over F₅ — Digital

Digital (71, 117, 276)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 117, 8456)-Net in Base 5 — Upper bound on s

There is no (71, 117, 8457)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6034 081974 584612 741267 631904 144569 262592 988992 301349 419131 755376 789958 047039 357325 > 5¹¹⁷ [i]