MinT - Best Known (127−49, 127, s)-Nets in Base 5

Best Known (127−49, 127, s)-Nets in Base 5

(127−49, 127, 252)-Net over F₅ — Constructive and digital

Digital (78, 127, 252)-net over F₅, using

9 times m-reduction [i] based on digital (78, 136, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 68, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(127−49, 127, 317)-Net over F₅ — Digital

Digital (78, 127, 317)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−49, 127, 11434)-Net in Base 5 — Upper bound on s

There is no (78, 127, 11435)-net in base 5, because

1 times m-reduction [i] would yield (78, 126, 11435)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11757 976312 713447 679903 419809 715548 748349 351899 676281 168835 628526 537230 194663 043114 015905 > 5¹²⁶ [i]