MinT - Best Known (59, 59+49, s)-Nets in Base 5

Best Known (59, 59+49, s)-Nets in Base 5

(59, 59+49, 132)-Net over F₅ — Constructive and digital

Digital (59, 108, 132)-net over F₅, using

2 times m-reduction [i] based on digital (59, 110, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 55, 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]

(59, 59+49, 155)-Net over F₅ — Digital

Digital (59, 108, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+49, 3185)-Net in Base 5 — Upper bound on s

There is no (59, 108, 3186)-net in base 5, because

1 times m-reduction [i] would yield (59, 107, 3186)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 618 893562 707005 819189 830430 981943 025826 432835 533391 033372 287584 217595 639425 > 5¹⁰⁷ [i]