MinT - Best Known (69, 128, s)-Nets in Base 5

Best Known (69, 128, s)-Nets in Base 5

(69, 128, 132)-Net over F₅ — Constructive and digital

Digital (69, 128, 132)-net over F₅, using

2 times m-reduction [i] based on digital (69, 130, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 65, 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]

(69, 128, 168)-Net over F₅ — Digital

Digital (69, 128, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 128, 3336)-Net in Base 5 — Upper bound on s

There is no (69, 128, 3337)-net in base 5, because

1 times m-reduction [i] would yield (69, 127, 3337)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58924 837829 032401 850539 744972 432429 421933 666418 157096 620075 617271 668811 146393 793877 037685 > 5¹²⁷ [i]