MinT - Best Known (56, 56+29, s)-Nets in Base 5

Best Known (56, 56+29, s)-Nets in Base 5

(56, 56+29, 252)-Net over F₅ — Constructive and digital

Digital (56, 85, 252)-net over F₅, using

7 times m-reduction [i] based on digital (56, 92, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 46, 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]

(56, 56+29, 388)-Net over F₅ — Digital

Digital (56, 85, 388)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+29, 23606)-Net in Base 5 — Upper bound on s

There is no (56, 85, 23607)-net in base 5, because

1 times m-reduction [i] would yield (56, 84, 23607)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51710 333934 089535 312142 169783 329366 882246 552307 406707 201225 > 5⁸⁴ [i]