MinT - Best Known (97−34, 97, s)-Nets in Base 5

Best Known (97−34, 97, s)-Nets in Base 5

(97−34, 97, 252)-Net over F₅ — Constructive and digital

Digital (63, 97, 252)-net over F₅, using

9 times m-reduction [i] based on digital (63, 106, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 53, 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]

(97−34, 97, 380)-Net over F₅ — Digital

Digital (63, 97, 380)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−34, 97, 17451)-Net in Base 5 — Upper bound on s

There is no (63, 97, 17452)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 63 168271 416007 433663 882089 554900 822320 741415 297616 123135 737166 991025 > 5⁹⁷ [i]