MinT - Best Known (175, 175+75, s)-Nets in Base 4

Best Known (175, 175+75, s)-Nets in Base 4

(175, 175+75, 531)-Net over F₄ — Constructive and digital

Digital (175, 250, 531)-net over F₄, using

2 times m-reduction [i] based on digital (175, 252, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 84, 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]

(175, 175+75, 1005)-Net over F₄ — Digital

Digital (175, 250, 1005)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+75, 54985)-Net in Base 4 — Upper bound on s

There is no (175, 250, 54986)-net in base 4, because

1 times m-reduction [i] would yield (175, 249, 54986)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818348 811370 876553 468844 126703 579814 529614 809750 185456 262182 548755 281084 663048 865837 274761 401624 910359 477081 360871 049938 136717 085498 580241 532757 277668 > 4²⁴⁹ [i]