MinT - Best Known (109−43, 109, s)-Nets in Base 5

Best Known (109−43, 109, s)-Nets in Base 5

(109−43, 109, 252)-Net over F₅ — Constructive and digital

Digital (66, 109, 252)-net over F₅, using

3 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 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]

(109−43, 109, 258)-Net over F₅ — Digital

Digital (66, 109, 258)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−43, 109, 8518)-Net in Base 5 — Upper bound on s

There is no (66, 109, 8519)-net in base 5, because

1 times m-reduction [i] would yield (66, 108, 8519)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3085 872507 344388 454761 213728 120809 175668 623325 898622 268879 173917 660390 443725 > 5¹⁰⁸ [i]