MinT - Best Known (101−28, 101, s)-Nets in Base 5

Best Known (101−28, 101, s)-Nets in Base 5

(101−28, 101, 296)-Net over F₅ — Constructive and digital

Digital (73, 101, 296)-net over F₅, using

7 times m-reduction [i] based on digital (73, 108, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 54, 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]

(101−28, 101, 1138)-Net over F₅ — Digital

Digital (73, 101, 1138)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−28, 101, 166702)-Net in Base 5 — Upper bound on s

There is no (73, 101, 166703)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 39446 098274 777986 023580 516918 770767 314571 997013 657049 405625 171909 230025 > 5¹⁰¹ [i]