MinT - Best Known (80−36, 80, s)-Nets in Base 5

Best Known (80−36, 80, s)-Nets in Base 5

(80−36, 80, 132)-Net over F₅ — Constructive and digital

Digital (44, 80, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 40, 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]

(80−36, 80, 2400)-Net in Base 5 — Upper bound on s

There is no (44, 80, 2401)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 83 162516 836687 225392 028037 294131 930464 519559 074973 156825 > 5⁸⁰ [i]