MinT - Best Known (61, 61+53, s)-Nets in Base 5

Best Known (61, 61+53, s)-Nets in Base 5

(61, 61+53, 132)-Net over F₅ — Constructive and digital

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]

(61, 61+53, 148)-Net over F₅ — Digital

Digital (61, 114, 148)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+53, 2858)-Net in Base 5 — Upper bound on s

There is no (61, 114, 2859)-net in base 5, because

1 times m-reduction [i] would yield (61, 113, 2859)-net in base 5, but
- 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]