MinT - Best Known (67, 67+51, s)-Nets in Base 5

Best Known (67, 67+51, s)-Nets in Base 5

(67, 67+51, 132)-Net over F₅ — Constructive and digital

Digital (67, 118, 132)-net over F₅, using

8 times m-reduction [i] based on digital (67, 126, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 63, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(67, 67+51, 198)-Net over F₅ — Digital

Digital (67, 118, 198)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+51, 4732)-Net in Base 5 — Upper bound on s

There is no (67, 118, 4733)-net in base 5, because

1 times m-reduction [i] would yield (67, 117, 4733)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6039 398448 016077 254263 469000 780573 470730 645457 567054 201472 796410 775983 856570 565141 > 5¹¹⁷ [i]