MinT - Best Known (146, 146+59, s)-Nets in Base 4

Best Known (146, 146+59, s)-Nets in Base 4

(146, 146+59, 531)-Net over F₄ — Constructive and digital

Digital (146, 205, 531)-net over F₄, using

t-expansion [i] based on digital (145, 205, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 69, 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]

(146, 146+59, 1010)-Net over F₄ — Digital

Digital (146, 205, 1010)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+59, 66838)-Net in Base 4 — Upper bound on s

There is no (146, 205, 66839)-net in base 4, because

1 times m-reduction [i] would yield (146, 204, 66839)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 156192 721212 649469 362233 281003 131154 708994 652368 530564 759364 477322 588091 364564 564639 107568 850112 084470 334014 715472 604992 > 4²⁰⁴ [i]