MinT - Best Known (109, 145, s)-Nets in Base 4

Best Known (109, 145, s)-Nets in Base 4

(109, 145, 1028)-Net over F₄ — Constructive and digital

Digital (109, 145, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (108, 144, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 36, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(109, 145, 1464)-Net over F₄ — Digital

Digital (109, 145, 1464)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 145, 178197)-Net in Base 4 — Upper bound on s

There is no (109, 145, 178198)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 429124 889102 671082 585733 912179 038618 782839 108013 395552 371206 111108 524244 881816 926570 > 4¹⁴⁵ [i]