MinT - Best Known (106−30, 106, s)-Nets in Base 5

Best Known (106−30, 106, s)-Nets in Base 5

(106−30, 106, 296)-Net over F₅ — Constructive and digital

Digital (76, 106, 296)-net over F₅, using

8 times m-reduction [i] based on digital (76, 114, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 57, 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]

(106−30, 106, 1061)-Net over F₅ — Digital

Digital (76, 106, 1061)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−30, 106, 139656)-Net in Base 5 — Upper bound on s

There is no (76, 106, 139657)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123 265714 587487 497758 016684 979033 105888 878975 822743 439881 690709 446019 106605 > 5¹⁰⁶ [i]