MinT - Best Known (129−49, 129, s)-Nets in Base 5

Best Known (129−49, 129, s)-Nets in Base 5

(129−49, 129, 252)-Net over F₅ — Constructive and digital

Digital (80, 129, 252)-net over F₅, using

11 times m-reduction [i] based on digital (80, 140, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 70, 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]

(129−49, 129, 341)-Net over F₅ — Digital

Digital (80, 129, 341)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−49, 129, 13078)-Net in Base 5 — Upper bound on s

There is no (80, 129, 13079)-net in base 5, because

1 times m-reduction [i] would yield (80, 128, 13079)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 294071 788867 821333 471765 470900 952806 307016 170075 084596 050690 069697 091032 847488 512660 702625 > 5¹²⁸ [i]