MinT - Best Known (145−41, 145, s)-Nets in Base 4

Best Known (145−41, 145, s)-Nets in Base 4

(145−41, 145, 531)-Net over F₄ — Constructive and digital

Digital (104, 145, 531)-net over F₄, using

4¹ times duplication [i] based on digital (103, 144, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 48, 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]

(145−41, 145, 820)-Net over F₄ — Digital

Digital (104, 145, 820)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−41, 145, 59827)-Net in Base 4 — Upper bound on s

There is no (104, 145, 59828)-net in base 4, because

1 times m-reduction [i] would yield (104, 144, 59828)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 435422 296450 339747 441002 686435 305297 640615 930682 733655 056499 199919 703479 832921 588456 > 4¹⁴⁴ [i]