MinT - Best Known (117−45, 117, s)-Nets in Base 5

Best Known (117−45, 117, s)-Nets in Base 5

(117−45, 117, 252)-Net over F₅ — Constructive and digital

Digital (72, 117, 252)-net over F₅, using

7 times m-reduction [i] based on digital (72, 124, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 62, 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]

(117−45, 117, 300)-Net over F₅ — Digital

Digital (72, 117, 300)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−45, 117, 10955)-Net in Base 5 — Upper bound on s

There is no (72, 117, 10956)-net in base 5, because

1 times m-reduction [i] would yield (72, 116, 10956)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1204 573964 112170 535946 627427 894349 785957 444552 447931 841997 603017 336009 460337 865025 > 5¹¹⁶ [i]