MinT - Best Known (154−41, 154, s)-Nets in Base 4

Best Known (154−41, 154, s)-Nets in Base 4

(154−41, 154, 531)-Net over F₄ — Constructive and digital

Digital (113, 154, 531)-net over F₄, using

5 times m-reduction [i] based on digital (113, 159, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 53, 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]

(154−41, 154, 1113)-Net over F₄ — Digital

Digital (113, 154, 1113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−41, 154, 111655)-Net in Base 4 — Upper bound on s

There is no (113, 154, 111656)-net in base 4, because

1 times m-reduction [i] would yield (113, 153, 111656)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 376481 185049 356911 480194 490842 291881 726293 350171 784276 807581 846518 791478 990184 789278 916634 > 4¹⁵³ [i]