MinT - Best Known (74, 74+55, s)-Nets in Base 5

Best Known (74, 74+55, s)-Nets in Base 5

(74, 74+55, 208)-Net over F₅ — Constructive and digital

Digital (74, 129, 208)-net over F₅, using

1 times m-reduction [i] based on digital (74, 130, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 65, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(74, 74+55, 224)-Net over F₅ — Digital

Digital (74, 129, 224)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+55, 5603)-Net in Base 5 — Upper bound on s

There is no (74, 129, 5604)-net in base 5, because

1 times m-reduction [i] would yield (74, 128, 5604)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 294637 022361 442022 738672 195246 625624 201388 232071 513385 247419 564194 910085 509920 041992 827793 > 5¹²⁸ [i]