MinT - Best Known (67, 127, s)-Nets in Base 5

Best Known (67, 127, s)-Nets in Base 5

(67, 127, 104)-Net over F₅ — Constructive and digital

Digital (67, 127, 104)-net over F₅, using

1 times m-reduction [i] based on digital (67, 128, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 64, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(67, 127, 153)-Net over F₅ — Digital

Digital (67, 127, 153)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 127, 2717)-Net in Base 5 — Upper bound on s

There is no (67, 127, 2718)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58932 765481 873127 827586 925119 474477 815128 739954 937617 531052 036701 797045 104078 206136 787009 > 5¹²⁷ [i]