MinT - Best Known (75−25, 75, s)-Nets in Base 5

Best Known (75−25, 75, s)-Nets in Base 5

(75−25, 75, 252)-Net over F₅ — Constructive and digital

Digital (50, 75, 252)-net over F₅, using

5 times m-reduction [i] based on digital (50, 80, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 40, 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]

(75−25, 75, 386)-Net over F₅ — Digital

Digital (50, 75, 386)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−25, 75, 27007)-Net in Base 5 — Upper bound on s

There is no (50, 75, 27008)-net in base 5, because

1 times m-reduction [i] would yield (50, 74, 27008)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5295 802318 836919 676292 092412 727106 118965 729899 085825 > 5⁷⁴ [i]