MinT - Best Known (43, 43+20, s)-Nets in Base 5

Best Known (43, 43+20, s)-Nets in Base 5

(43, 43+20, 252)-Net over F₅ — Constructive and digital

Digital (43, 63, 252)-net over F₅, using

3 times m-reduction [i] based on digital (43, 66, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 33, 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]

(43, 43+20, 421)-Net over F₅ — Digital

Digital (43, 63, 421)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+20, 28662)-Net in Base 5 — Upper bound on s

There is no (43, 63, 28663)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 108 421076 190045 377513 308524 922650 783974 246361 > 5⁶³ [i]