MinT - Best Known (52, 52+44, s)-Nets in Base 5

Best Known (52, 52+44, s)-Nets in Base 5

(52, 52+44, 132)-Net over F₅ — Constructive and digital

Digital (52, 96, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 48, 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]

(52, 52+44, 136)-Net over F₅ — Digital

Digital (52, 96, 136)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+44, 2524)-Net in Base 5 — Upper bound on s

There is no (52, 96, 2525)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 720953 369893 791012 176367 663569 938437 850596 435899 917827 471428 995401 > 5⁹⁶ [i]