MinT - Best Known (88−40, 88, s)-Nets in Base 5

Best Known (88−40, 88, s)-Nets in Base 5

(88−40, 88, 132)-Net over F₅ — Constructive and digital

Digital (48, 88, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 44, 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]

(88−40, 88, 2455)-Net in Base 5 — Upper bound on s

There is no (48, 88, 2456)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 32 408917 145953 641248 163687 285977 280166 496296 853634 810149 023745 > 5⁸⁸ [i]