MinT - Best Known (96, 96+40, s)-Nets in Base 5

Best Known (96, 96+40, s)-Nets in Base 5

(96, 96+40, 400)-Net over F₅ — Constructive and digital

Digital (96, 136, 400)-net over F₅, using

6 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]

(96, 96+40, 1073)-Net over F₅ — Digital

Digital (96, 136, 1073)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+40, 117540)-Net in Base 5 — Upper bound on s

There is no (96, 136, 117541)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114797 973661 642250 632280 718342 508396 306337 429390 586587 389875 962168 350510 585825 672574 252013 728945 > 5¹³⁶ [i]