MinT - Best Known (114−34, 114, s)-Nets in Base 5

Best Known (114−34, 114, s)-Nets in Base 5

(114−34, 114, 296)-Net over F₅ — Constructive and digital

Digital (80, 114, 296)-net over F₅, using

8 times m-reduction [i] based on digital (80, 122, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 61, 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]

(114−34, 114, 871)-Net over F₅ — Digital

Digital (80, 114, 871)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−34, 114, 87304)-Net in Base 5 — Upper bound on s

There is no (80, 114, 87305)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 156190 628549 372729 830248 579879 553971 670123 028835 549851 908794 684254 719010 188005 > 5¹¹⁴ [i]