MinT - Best Known (161−40, 161, s)-Nets in Base 4

Best Known (161−40, 161, s)-Nets in Base 4

(161−40, 161, 1028)-Net over F₄ — Constructive and digital

Digital (121, 161, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (120, 160, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 40, 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]

(161−40, 161, 1589)-Net over F₄ — Digital

Digital (121, 161, 1589)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−40, 161, 194415)-Net in Base 4 — Upper bound on s

There is no (121, 161, 194416)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 544030 106965 903014 836481 219279 301127 632544 143818 732410 457050 710240 628116 482918 776658 922978 156934 > 4¹⁶¹ [i]