MinT - Best Known (72, 72+31, s)-Nets in Base 5

Best Known (72, 72+31, s)-Nets in Base 5

(72, 72+31, 296)-Net over F₅ — Constructive and digital

Digital (72, 103, 296)-net over F₅, using

3 times m-reduction [i] based on digital (72, 106, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 53, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(72, 72+31, 771)-Net over F₅ — Digital

Digital (72, 103, 771)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+31, 90918)-Net in Base 5 — Upper bound on s

There is no (72, 103, 90919)-net in base 5, because

1 times m-reduction [i] would yield (72, 102, 90919)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197237 814353 207099 050730 512935 034113 697929 625571 148637 489110 397130 009829 > 5¹⁰² [i]