MinT - Best Known (74, 74+63, s)-Nets in Base 5

Best Known (74, 74+63, s)-Nets in Base 5

(74, 74+63, 132)-Net over F₅ — Constructive and digital

Digital (74, 137, 132)-net over F₅, using

3 times m-reduction [i] based on digital (74, 140, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 70, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(74, 74+63, 179)-Net over F₅ — Digital

Digital (74, 137, 179)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+63, 3594)-Net in Base 5 — Upper bound on s

There is no (74, 137, 3595)-net in base 5, because

1 times m-reduction [i] would yield (74, 136, 3595)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114879 635735 308915 713097 600915 484446 789525 112479 959178 742044 411258 134761 649345 908399 528994 525429 > 5¹³⁶ [i]