MinT - Best Known (248−58, 248, s)-Nets in Base 4

Best Known (248−58, 248, s)-Nets in Base 4

(248−58, 248, 1044)-Net over F₄ — Constructive and digital

Digital (190, 248, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 62, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(248−58, 248, 3093)-Net over F₄ — Digital

Digital (190, 248, 3093)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−58, 248, 547813)-Net in Base 4 — Upper bound on s

There is no (190, 248, 547814)-net in base 4, because

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]