MinT - Best Known (88, 88+53, s)-Nets in Base 5

Best Known (88, 88+53, s)-Nets in Base 5

(88, 88+53, 252)-Net over F₅ — Constructive and digital

Digital (88, 141, 252)-net over F₅, using

t-expansion [i] based on digital (85, 141, 252)-net over F₅, using
- 9 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]

(88, 88+53, 383)-Net over F₅ — Digital

Digital (88, 141, 383)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+53, 15288)-Net in Base 5 — Upper bound on s

There is no (88, 141, 15289)-net in base 5, because

1 times m-reduction [i] would yield (88, 140, 15289)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 748742 657797 182544 418495 525730 556240 141866 396005 809938 214501 954994 369380 224809 213355 539211 080633 > 5¹⁴⁰ [i]