MinT - Best Known (72, 72+53, s)-Nets in Base 5

Best Known (72, 72+53, s)-Nets in Base 5

(72, 72+53, 208)-Net over F₅ — Constructive and digital

Digital (72, 125, 208)-net over F₅, using

1 times m-reduction [i] based on digital (72, 126, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 63, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(72, 72+53, 222)-Net over F₅ — Digital

Digital (72, 125, 222)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+53, 5666)-Net in Base 5 — Upper bound on s

There is no (72, 125, 5667)-net in base 5, because

1 times m-reduction [i] would yield (72, 124, 5667)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 840451 139487 823412 290874 103197 229920 396450 501400 135007 195337 897394 728731 879556 270361 > 5¹²⁴ [i]