MinT - Best Known (112−37, 112, s)-Nets in Base 5

Best Known (112−37, 112, s)-Nets in Base 5

(112−37, 112, 296)-Net over F₅ — Constructive and digital

Digital (75, 112, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 56, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(112−37, 112, 551)-Net over F₅ — Digital

Digital (75, 112, 551)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−37, 112, 38569)-Net in Base 5 — Upper bound on s

There is no (75, 112, 38570)-net in base 5, because

1 times m-reduction [i] would yield (75, 111, 38570)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385359 770837 286743 079228 732828 860618 937395 804353 958002 088845 260346 659434 031809 > 5¹¹¹ [i]