MinT - Best Known (94−41, 94, s)-Nets in Base 5

Best Known (94−41, 94, s)-Nets in Base 5

(94−41, 94, 132)-Net over F₅ — Constructive and digital

Digital (53, 94, 132)-net over F₅, using

4 times m-reduction [i] based on digital (53, 98, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 49, 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]

(94−41, 94, 160)-Net over F₅ — Digital

Digital (53, 94, 160)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−41, 94, 3679)-Net in Base 5 — Upper bound on s

There is no (53, 94, 3680)-net in base 5, because

1 times m-reduction [i] would yield (53, 93, 3680)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101423 911512 860243 341659 525731 295230 570712 907824 334330 622339 805185 > 5⁹³ [i]