MinT - Best Known (146−67, 146, s)-Nets in Base 5

Best Known (146−67, 146, s)-Nets in Base 5

(146−67, 146, 132)-Net over F₅ — Constructive and digital

Digital (79, 146, 132)-net over F₅, using

4 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 75, 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]

(146−67, 146, 191)-Net over F₅ — Digital

Digital (79, 146, 191)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−67, 146, 3853)-Net in Base 5 — Upper bound on s

There is no (79, 146, 3854)-net in base 5, because

1 times m-reduction [i] would yield (79, 145, 3854)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 225982 947455 895314 904537 323057 516244 346195 969618 643437 324014 950040 799861 791390 058398 695168 169721 310265 > 5¹⁴⁵ [i]