MinT - Best Known (145−54, 145, s)-Nets in Base 5

Best Known (145−54, 145, s)-Nets in Base 5

(145−54, 145, 252)-Net over F₅ — Constructive and digital

Digital (91, 145, 252)-net over F₅, using

t-expansion [i] based on digital (85, 145, 252)-net over F₅, using
- 5 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]

(145−54, 145, 406)-Net over F₅ — Digital

Digital (91, 145, 406)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−54, 145, 15471)-Net in Base 5 — Upper bound on s

There is no (91, 145, 15472)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224565 530273 174345 831618 335565 288929 685535 548045 016686 140451 104395 890265 119046 013074 155755 589590 642625 > 5¹⁴⁵ [i]