MinT - Best Known (60, 60+30, s)-Nets in Base 5

Best Known (60, 60+30, s)-Nets in Base 5

(60, 60+30, 252)-Net over F₅ — Constructive and digital

Digital (60, 90, 252)-net over F₅, using

10 times m-reduction [i] based on digital (60, 100, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 50, 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]

(60, 60+30, 445)-Net over F₅ — Digital

Digital (60, 90, 445)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+30, 25080)-Net in Base 5 — Upper bound on s

There is no (60, 90, 25081)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 807 912076 899570 354229 820514 084713 387636 035962 782122 099881 219565 > 5⁹⁰ [i]