MinT - Best Known (160−52, 160, s)-Nets in Base 4

Best Known (160−52, 160, s)-Nets in Base 4

(160−52, 160, 240)-Net over F₄ — Constructive and digital

Digital (108, 160, 240)-net over F₄, using

4¹ times duplication [i] based on digital (107, 159, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 53, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(160−52, 160, 500)-Net over F₄ — Digital

Digital (108, 160, 500)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−52, 160, 17809)-Net in Base 4 — Upper bound on s

There is no (108, 160, 17810)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 138952 863813 619844 649688 143478 090176 416608 512191 767482 672818 901160 578875 877415 723098 553704 896960 > 4¹⁶⁰ [i]