MinT - Best Known (138−38, 138, s)-Nets in Base 5

Best Known (138−38, 138, s)-Nets in Base 5

(138−38, 138, 408)-Net over F₅ — Constructive and digital

Digital (100, 138, 408)-net over F₅, using

2 times m-reduction [i] based on digital (100, 140, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 70, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(138−38, 138, 1500)-Net over F₅ — Digital

Digital (100, 138, 1500)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−38, 138, 236515)-Net in Base 5 — Upper bound on s

There is no (100, 138, 236516)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 869953 673168 380375 442177 643133 912052 238721 341529 054867 129986 454514 909280 397807 520100 855264 276625 > 5¹³⁸ [i]