MinT - Best Known (62−27, 62, s)-Nets in Base 5

Best Known (62−27, 62, s)-Nets in Base 5

(62−27, 62, 132)-Net over F₅ — Constructive and digital

Digital (35, 62, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 31, 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]

(62−27, 62, 2689)-Net in Base 5 — Upper bound on s

There is no (35, 62, 2690)-net in base 5, because

1 times m-reduction [i] would yield (35, 61, 2690)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 351467 331527 152750 504123 363559 529229 256201 > 5⁶¹ [i]