MinT - Best Known (69, 69+61, s)-Nets in Base 5

Best Known (69, 69+61, s)-Nets in Base 5

(69, 69+61, 132)-Net over F₅ — Constructive and digital

Digital (69, 130, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 65, 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]

(69, 69+61, 160)-Net over F₅ — Digital

Digital (69, 130, 160)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+61, 3028)-Net in Base 5 — Upper bound on s

There is no (69, 130, 3029)-net in base 5, because

1 times m-reduction [i] would yield (69, 129, 3029)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 483078 231386 201261 128676 955669 552421 087225 576645 461338 560919 393315 548401 824584 441470 077225 > 5¹²⁹ [i]