MinT - Best Known (118−52, 118, s)-Nets in Base 5

Best Known (118−52, 118, s)-Nets in Base 5

(118−52, 118, 132)-Net over F₅ — Constructive and digital

Digital (66, 118, 132)-net over F₅, using

6 times m-reduction [i] based on digital (66, 124, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 62, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(118−52, 118, 184)-Net over F₅ — Digital

Digital (66, 118, 184)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−52, 118, 3902)-Net in Base 5 — Upper bound on s

There is no (66, 118, 3903)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30133 050225 419975 833579 514144 902201 204501 838822 273963 247618 048988 198776 852627 353497 > 5¹¹⁸ [i]