MinT - Best Known (110−49, 110, s)-Nets in Base 5

Best Known (110−49, 110, s)-Nets in Base 5

(110−49, 110, 132)-Net over F₅ — Constructive and digital

Digital (61, 110, 132)-net over F₅, using

4 times m-reduction [i] based on digital (61, 114, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 57, 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]

(110−49, 110, 168)-Net over F₅ — Digital

Digital (61, 110, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−49, 110, 3645)-Net in Base 5 — Upper bound on s

There is no (61, 110, 3646)-net in base 5, because

1 times m-reduction [i] would yield (61, 109, 3646)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15493 781711 333159 436526 197858 269394 341790 419185 144059 399322 437272 631752 298625 > 5¹⁰⁹ [i]