MinT - Best Known (143−61, 143, s)-Nets in Base 5

Best Known (143−61, 143, s)-Nets in Base 5

(143−61, 143, 252)-Net over F₅ — Constructive and digital

Digital (82, 143, 252)-net over F₅, using

1 times m-reduction [i] based on digital (82, 144, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 72, 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]

(143−61, 143, 6104)-Net in Base 5 — Upper bound on s

There is no (82, 143, 6105)-net in base 5, because

1 times m-reduction [i] would yield (82, 142, 6105)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1801 009494 903092 223217 468806 494587 081310 886186 585499 914598 808544 831754 233535 952569 526845 004566 774185 > 5¹⁴² [i]