MinT - Best Known (119−39, 119, s)-Nets in Base 5

Best Known (119−39, 119, s)-Nets in Base 5

(119−39, 119, 296)-Net over F₅ — Constructive and digital

Digital (80, 119, 296)-net over F₅, using

3 times m-reduction [i] based on digital (80, 122, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 61, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(119−39, 119, 597)-Net over F₅ — Digital

Digital (80, 119, 597)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−39, 119, 43449)-Net in Base 5 — Upper bound on s

There is no (80, 119, 43450)-net in base 5, because

1 times m-reduction [i] would yield (80, 118, 43450)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30092 730879 726487 795152 276429 224651 946290 375014 222807 095747 958802 799300 834487 501961 > 5¹¹⁸ [i]