MinT - Best Known (42, 42+21, s)-Nets in Base 5

Best Known (42, 42+21, s)-Nets in Base 5

(42, 42+21, 252)-Net over F₅ — Constructive and digital

Digital (42, 63, 252)-net over F₅, using

1 times m-reduction [i] based on digital (42, 64, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 32, 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]

(42, 42+21, 340)-Net over F₅ — Digital

Digital (42, 63, 340)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+21, 24400)-Net in Base 5 — Upper bound on s

There is no (42, 63, 24401)-net in base 5, because

1 times m-reduction [i] would yield (42, 62, 24401)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 21 684963 434841 162223 495652 646550 873887 707385 > 5⁶² [i]