MinT - Best Known (113−52, 113, s)-Nets in Base 5

Best Known (113−52, 113, s)-Nets in Base 5

(113−52, 113, 132)-Net over F₅ — Constructive and digital

Digital (61, 113, 132)-net over F₅, using

1 times m-reduction [i] based on digital (61, 114, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 57, 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]

(113−52, 113, 152)-Net over F₅ — Digital

Digital (61, 113, 152)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−52, 113, 2858)-Net in Base 5 — Upper bound on s

There is no (61, 113, 2859)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 641065 876418 047249 863387 059835 377161 914705 043567 178518 877444 266900 474869 736217 > 5¹¹³ [i]