MinT - Best Known (84−36, 84, s)-Nets in Base 5

Best Known (84−36, 84, s)-Nets in Base 5

(84−36, 84, 132)-Net over F₅ — Constructive and digital

Digital (48, 84, 132)-net over F₅, using

4 times m-reduction [i] based on 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]

(84−36, 84, 155)-Net over F₅ — Digital

Digital (48, 84, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−36, 84, 3437)-Net in Base 5 — Upper bound on s

There is no (48, 84, 3438)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51725 886803 751229 913409 108144 336713 197330 015457 479716 186625 > 5⁸⁴ [i]