MinT - Best Known (112−38, 112, s)-Nets in Base 5

Best Known (112−38, 112, s)-Nets in Base 5

(112−38, 112, 252)-Net over F₅ — Constructive and digital

Digital (74, 112, 252)-net over F₅, using

16 times m-reduction [i] based on digital (74, 128, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 64, 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]

(112−38, 112, 488)-Net over F₅ — Digital

Digital (74, 112, 488)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−38, 112, 26131)-Net in Base 5 — Upper bound on s

There is no (74, 112, 26132)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 926040 293868 727611 099149 247047 179741 672315 048171 358366 163644 255352 481109 452625 > 5¹¹² [i]