MinT - Best Known (104, 104+40, s)-Nets in Base 4

Best Known (104, 104+40, s)-Nets in Base 4

(104, 104+40, 531)-Net over F₄ — Constructive and digital

Digital (104, 144, 531)-net over F₄, using

t-expansion [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]

(104, 104+40, 877)-Net over F₄ — Digital

Digital (104, 144, 877)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+40, 59827)-Net in Base 4 — Upper bound on s

There is no (104, 144, 59828)-net in base 4, because

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]