MinT - Best Known (138−48, 138, s)-Nets in Base 5

Best Known (138−48, 138, s)-Nets in Base 5

(138−48, 138, 296)-Net over F₅ — Constructive and digital

Digital (90, 138, 296)-net over F₅, using

4 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 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]

(138−48, 138, 515)-Net over F₅ — Digital

Digital (90, 138, 515)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−48, 138, 25590)-Net in Base 5 — Upper bound on s

There is no (90, 138, 25591)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 870461 642837 301498 448385 233143 621227 688485 696044 299320 310101 400850 484463 807650 862713 014716 177825 > 5¹³⁸ [i]