MinT - Best Known (54, 54+29, s)-Nets in Base 5

Best Known (54, 54+29, s)-Nets in Base 5

(54, 54+29, 252)-Net over F₅ — Constructive and digital

Digital (54, 83, 252)-net over F₅, using

5 times m-reduction [i] based on digital (54, 88, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 44, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(54, 54+29, 346)-Net over F₅ — Digital

Digital (54, 83, 346)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+29, 18755)-Net in Base 5 — Upper bound on s

There is no (54, 83, 18756)-net in base 5, because

1 times m-reduction [i] would yield (54, 82, 18756)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2068 401591 597136 955755 527874 414831 401950 681228 688217 490625 > 5⁸² [i]