MinT - Best Known (109−49, 109, s)-Nets in Base 5

Best Known (109−49, 109, s)-Nets in Base 5

(109−49, 109, 132)-Net over F₅ — Constructive and digital

Digital (60, 109, 132)-net over F₅, using

3 times m-reduction [i] based on digital (60, 112, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 56, 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]

(109−49, 109, 161)-Net over F₅ — Digital

Digital (60, 109, 161)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−49, 109, 3407)-Net in Base 5 — Upper bound on s

There is no (60, 109, 3408)-net in base 5, because

1 times m-reduction [i] would yield (60, 108, 3408)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3090 379358 800590 700522 339317 341159 361310 740719 349203 358081 526706 439102 183425 > 5¹⁰⁸ [i]