MinT - Best Known (138−42, 138, s)-Nets in Base 5

Best Known (138−42, 138, s)-Nets in Base 5

(138−42, 138, 400)-Net over F₅ — Constructive and digital

Digital (96, 138, 400)-net over F₅, using

4 times m-reduction [i] based on digital (96, 142, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 71, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(138−42, 138, 929)-Net over F₅ — Digital

Digital (96, 138, 929)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−42, 138, 85032)-Net in Base 5 — Upper bound on s

There is no (96, 138, 85033)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 870045 734391 360618 605778 702853 761602 151008 120945 698188 045317 507468 975334 854869 748485 317730 020245 > 5¹³⁸ [i]