MinT - Best Known (228−68, 228, s)-Nets in Base 4

Best Known (228−68, 228, s)-Nets in Base 4

(228−68, 228, 531)-Net over F₄ — Constructive and digital

Digital (160, 228, 531)-net over F₄, using

t-expansion [i] based on digital (159, 228, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 76, 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]

(228−68, 228, 950)-Net over F₄ — Digital

Digital (160, 228, 950)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−68, 228, 49141)-Net in Base 4 — Upper bound on s

There is no (160, 228, 49142)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186085 815986 324858 502771 728835 222660 430606 811319 577485 514509 395075 465019 347912 837694 034201 778284 671008 342216 800950 028429 277473 174485 860098 > 4²²⁸ [i]