MinT - Best Known (48−20, 48, s)-Nets in Base 5

Best Known (48−20, 48, s)-Nets in Base 5

(48−20, 48, 132)-Net over F₅ — Constructive and digital

Digital (28, 48, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 24, 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]

(48−20, 48, 2557)-Net in Base 5 — Upper bound on s

There is no (28, 48, 2558)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3562 038291 038508 044003 489694 245505 > 5⁴⁸ [i]