MinT - Best Known (114−35, 114, s)-Nets in Base 5

Best Known (114−35, 114, s)-Nets in Base 5

(114−35, 114, 296)-Net over F₅ — Constructive and digital

Digital (79, 114, 296)-net over F₅, using

6 times m-reduction [i] based on digital (79, 120, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 60, 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]

(114−35, 114, 763)-Net over F₅ — Digital

Digital (79, 114, 763)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−35, 114, 79416)-Net in Base 5 — Upper bound on s

There is no (79, 114, 79417)-net in base 5, because

1 times m-reduction [i] would yield (79, 113, 79417)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 629841 172962 627365 949757 807858 701429 620137 317958 031596 460729 725760 166335 512485 > 5¹¹³ [i]