MinT - Best Known (122−56, 122, s)-Nets in Base 5

Best Known (122−56, 122, s)-Nets in Base 5

(122−56, 122, 132)-Net over F₅ — Constructive and digital

Digital (66, 122, 132)-net over F₅, using

2 times m-reduction [i] based on digital (66, 124, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 62, 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]

(122−56, 122, 164)-Net over F₅ — Digital

Digital (66, 122, 164)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−56, 122, 3116)-Net in Base 5 — Upper bound on s

There is no (66, 122, 3117)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 18 953869 007682 138991 293520 964514 845819 090949 237505 252356 625527 765996 399107 836289 976465 > 5¹²² [i]