MinT - Best Known (160−46, 160, s)-Nets in Base 4

Best Known (160−46, 160, s)-Nets in Base 4

(160−46, 160, 531)-Net over F₄ — Constructive and digital

Digital (114, 160, 531)-net over F₄, using

4¹ times duplication [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]

(160−46, 160, 830)-Net over F₄ — Digital

Digital (114, 160, 830)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−46, 160, 48463)-Net in Base 4 — Upper bound on s

There is no (114, 160, 48464)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136895 762660 306600 322701 143620 599110 322496 849346 070469 279069 619328 053344 213855 251073 415022 493092 > 4¹⁶⁰ [i]