MinT - Best Known (103−39, 103, s)-Nets in Base 5

Best Known (103−39, 103, s)-Nets in Base 5

(103−39, 103, 252)-Net over F₅ — Constructive and digital

Digital (64, 103, 252)-net over F₅, using

5 times m-reduction [i] based on digital (64, 108, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 54, 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]

(103−39, 103, 289)-Net over F₅ — Digital

Digital (64, 103, 289)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−39, 103, 11194)-Net in Base 5 — Upper bound on s

There is no (64, 103, 11195)-net in base 5, because

1 times m-reduction [i] would yield (64, 102, 11195)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197527 330456 949440 138316 850566 432689 601283 652070 850567 458752 542132 220389 > 5¹⁰² [i]