MinT - Best Known (140−53, 140, s)-Nets in Base 5

Best Known (140−53, 140, s)-Nets in Base 5

(140−53, 140, 252)-Net over F₅ — Constructive and digital

Digital (87, 140, 252)-net over F₅, using

t-expansion [i] based on digital (85, 140, 252)-net over F₅, using
- 10 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(140−53, 140, 370)-Net over F₅ — Digital

Digital (87, 140, 370)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−53, 140, 14370)-Net in Base 5 — Upper bound on s

There is no (87, 140, 14371)-net in base 5, because

1 times m-reduction [i] would yield (87, 139, 14371)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 371904 503823 801954 519356 563946 380056 204767 013143 799839 135962 293971 036023 926161 257831 816944 175385 > 5¹³⁹ [i]