MinT - Best Known (242−59, 242, s)-Nets in Base 4

Best Known (242−59, 242, s)-Nets in Base 4

(242−59, 242, 1032)-Net over F₄ — Constructive and digital

Digital (183, 242, 1032)-net over F₄, using

4² times duplication [i] based on digital (181, 240, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 60, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(242−59, 242, 2462)-Net over F₄ — Digital

Digital (183, 242, 2462)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−59, 242, 392013)-Net in Base 4 — Upper bound on s

There is no (183, 242, 392014)-net in base 4, because

1 times m-reduction [i] would yield (183, 241, 392014)-net in base 4, but
- 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]