MinT - Best Known (46, 68, s)-Nets in Base 5

Best Known (46, 68, s)-Nets in Base 5

(46, 68, 252)-Net over F₅ — Constructive and digital

Digital (46, 68, 252)-net over F₅, using

4 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]

(46, 68, 408)-Net over F₅ — Digital

Digital (46, 68, 408)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 68, 25687)-Net in Base 5 — Upper bound on s

There is no (46, 68, 25688)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 338827 231293 348574 139281 695304 687998 713604 440673 > 5⁶⁸ [i]