MinT - Best Known (249−59, 249, s)-Nets in Base 4

Best Known (249−59, 249, s)-Nets in Base 4

(249−59, 249, 1040)-Net over F₄ — Constructive and digital

Digital (190, 249, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (189, 248, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 62, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(249−59, 249, 2905)-Net over F₄ — Digital

Digital (190, 249, 2905)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−59, 249, 547813)-Net in Base 4 — Upper bound on s

There is no (190, 249, 547814)-net in base 4, because

1 times m-reduction [i] would yield (190, 248, 547814)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 204589 026874 342614 050862 224212 752663 726865 492751 985613 495656 748916 969243 162463 894988 537161 892093 489494 123054 244729 345268 399672 865070 618682 082008 128900 > 4²⁴⁸ [i]