MinT - Best Known (117−35, 117, s)-Nets in Base 5

Best Known (117−35, 117, s)-Nets in Base 5

(117−35, 117, 296)-Net over F₅ — Constructive and digital

Digital (82, 117, 296)-net over F₅, using

9 times m-reduction [i] based on digital (82, 126, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 63, 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]

(117−35, 117, 877)-Net over F₅ — Digital

Digital (82, 117, 877)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−35, 117, 105506)-Net in Base 5 — Upper bound on s

There is no (82, 117, 105507)-net in base 5, because

1 times m-reduction [i] would yield (82, 116, 105507)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1203 899206 948737 896208 293691 816741 224848 494883 869211 588863 809672 677126 921926 274125 > 5¹¹⁶ [i]