MinT - Best Known (146−49, 146, s)-Nets in Base 5

Best Known (146−49, 146, s)-Nets in Base 5

(146−49, 146, 296)-Net over F₅ — Constructive and digital

Digital (97, 146, 296)-net over F₅, using

t-expansion [i] based on digital (94, 146, 296)-net over F₅, using
- 4 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
  - trace code for nets [i] based on digital (19, 75, 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]

(146−49, 146, 629)-Net over F₅ — Digital

Digital (97, 146, 629)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−49, 146, 40931)-Net in Base 5 — Upper bound on s

There is no (97, 146, 40932)-net in base 5, because

1 times m-reduction [i] would yield (97, 145, 40932)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224233 200954 545339 324961 432754 684993 555703 703063 415517 416898 767667 827930 894246 500009 611109 923559 681025 > 5¹⁴⁵ [i]