MinT - Best Known (51, 51+32, s)-Nets in Base 5

Best Known (51, 51+32, s)-Nets in Base 5

(51, 51+32, 208)-Net over F₅ — Constructive and digital

Digital (51, 83, 208)-net over F₅, using

1 times m-reduction [i] based on digital (51, 84, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 42, 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]

(51, 51+32, 228)-Net over F₅ — Digital

Digital (51, 83, 228)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+32, 7172)-Net in Base 5 — Upper bound on s

There is no (51, 83, 7173)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10343 763436 980059 706625 216985 529432 103299 437106 813907 877313 > 5⁸³ [i]