MinT - Best Known (129−53, 129, s)-Nets in Base 5

Best Known (129−53, 129, s)-Nets in Base 5

(129−53, 129, 252)-Net over F₅ — Constructive and digital

Digital (76, 129, 252)-net over F₅, using

3 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(129−53, 129, 256)-Net over F₅ — Digital

Digital (76, 129, 256)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−53, 129, 7264)-Net in Base 5 — Upper bound on s

There is no (76, 129, 7265)-net in base 5, because

1 times m-reduction [i] would yield (76, 128, 7265)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 294802 761868 394695 135236 060188 808300 374699 787429 475695 994644 893924 114748 915442 045525 555385 > 5¹²⁸ [i]