MinT - Best Known (65, 65+49, s)-Nets in Base 5

Best Known (65, 65+49, s)-Nets in Base 5

(65, 65+49, 132)-Net over F₅ — Constructive and digital

Digital (65, 114, 132)-net over F₅, using

8 times m-reduction [i] based on digital (65, 122, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 61, 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]

(65, 65+49, 196)-Net over F₅ — Digital

Digital (65, 114, 196)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+49, 4771)-Net in Base 5 — Upper bound on s

There is no (65, 114, 4772)-net in base 5, because

1 times m-reduction [i] would yield (65, 113, 4772)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 630490 282127 781070 558071 332335 850387 990365 292712 497898 673803 189015 398637 210625 > 5¹¹³ [i]