MinT - Best Known (106, 145, s)-Nets in Base 4

Best Known (106, 145, s)-Nets in Base 4

(106, 145, 531)-Net over F₄ — Constructive and digital

Digital (106, 145, 531)-net over F₄, using

t-expansion [i] based on digital (105, 145, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (105, 147, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 49, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(106, 145, 1012)-Net over F₄ — Digital

Digital (106, 145, 1012)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 145, 96606)-Net in Base 4 — Upper bound on s

There is no (106, 145, 96607)-net in base 4, because

1 times m-reduction [i] would yield (106, 144, 96607)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 372807 964835 025462 919365 643514 400123 376850 625344 687768 769480 698391 649437 006199 260632 > 4¹⁴⁴ [i]