MinT - Best Known (68, 68+40, s)-Nets in Base 5

Best Known (68, 68+40, s)-Nets in Base 5

(68, 68+40, 252)-Net over F₅ — Constructive and digital

Digital (68, 108, 252)-net over F₅, using

8 times m-reduction [i] based on digital (68, 116, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 58, 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]

(68, 68+40, 327)-Net over F₅ — Digital

Digital (68, 108, 327)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+40, 12335)-Net in Base 5 — Upper bound on s

There is no (68, 108, 12336)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3081 496541 713745 827808 107060 400841 657406 990432 954677 586312 136612 887233 275905 > 5¹⁰⁸ [i]