MinT - Best Known (132−55, 132, s)-Nets in Base 5

Best Known (132−55, 132, s)-Nets in Base 5

(132−55, 132, 252)-Net over F₅ — Constructive and digital

Digital (77, 132, 252)-net over F₅, using

2 times m-reduction [i] based on digital (77, 134, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 67, 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]

(132−55, 132, 6704)-Net in Base 5 — Upper bound on s

There is no (77, 132, 6705)-net in base 5, because

1 times m-reduction [i] would yield (77, 131, 6705)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 800743 904288 589711 836349 872221 661549 497743 874077 985162 155331 356026 299474 672250 892347 194717 > 5¹³¹ [i]