MinT - Best Known (241−58, 241, s)-Nets in Base 4

Best Known (241−58, 241, s)-Nets in Base 4

(241−58, 241, 1036)-Net over F₄ — Constructive and digital

Digital (183, 241, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (182, 240, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 60, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(241−58, 241, 2613)-Net over F₄ — Digital

Digital (183, 241, 2613)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−58, 241, 392013)-Net in Base 4 — Upper bound on s

There is no (183, 241, 392014)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 487733 563403 152678 483922 167749 733449 002645 735719 078825 219825 549242 861444 418177 565356 832000 964870 744503 047816 959893 797826 173900 677772 162617 526396 > 4²⁴¹ [i]