MinT - Best Known (116−37, 116, s)-Nets in Base 5

Best Known (116−37, 116, s)-Nets in Base 5

(116−37, 116, 296)-Net over F₅ — Constructive and digital

Digital (79, 116, 296)-net over F₅, using

4 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]

(116−37, 116, 656)-Net over F₅ — Digital

Digital (79, 116, 656)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−37, 116, 55158)-Net in Base 5 — Upper bound on s

There is no (79, 116, 55159)-net in base 5, because

1 times m-reduction [i] would yield (79, 115, 55159)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 240 810689 926233 063438 126775 402317 857578 446418 105033 803613 510538 681365 887330 172345 > 5¹¹⁵ [i]