MinT - Best Known (59, 59+45, s)-Nets in Base 5

Best Known (59, 59+45, s)-Nets in Base 5

(59, 59+45, 132)-Net over F₅ — Constructive and digital

Digital (59, 104, 132)-net over F₅, using

6 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+45, 178)-Net over F₅ — Digital

Digital (59, 104, 178)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+45, 4222)-Net in Base 5 — Upper bound on s

There is no (59, 104, 4223)-net in base 5, because

1 times m-reduction [i] would yield (59, 103, 4223)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 986959 625801 351712 515680 840140 612057 736386 239740 318262 365389 411833 130921 > 5¹⁰³ [i]