MinT - Best Known (112−35, 112, s)-Nets in Base 5

Best Known (112−35, 112, s)-Nets in Base 5

(112−35, 112, 296)-Net over F₅ — Constructive and digital

Digital (77, 112, 296)-net over F₅, using

4 times m-reduction [i] based on digital (77, 116, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 58, 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]

(112−35, 112, 696)-Net over F₅ — Digital

Digital (77, 112, 696)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−35, 112, 65715)-Net in Base 5 — Upper bound on s

There is no (77, 112, 65716)-net in base 5, because

1 times m-reduction [i] would yield (77, 111, 65716)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385244 480140 865194 851409 401722 861627 463323 383640 161513 125664 775846 360431 471825 > 5¹¹¹ [i]