MinT - Best Known (71−25, 71, s)-Nets in Base 5

Best Known (71−25, 71, s)-Nets in Base 5

(71−25, 71, 252)-Net over F₅ — Constructive and digital

Digital (46, 71, 252)-net over F₅, using

1 times m-reduction [i] based on digital (46, 72, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 36, 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]

(71−25, 71, 298)-Net over F₅ — Digital

Digital (46, 71, 298)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−25, 71, 15790)-Net in Base 5 — Upper bound on s

There is no (46, 71, 15791)-net in base 5, because

1 times m-reduction [i] would yield (46, 70, 15791)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8 474273 880607 555990 612637 308589 552456 221911 921105 > 5⁷⁰ [i]