MinT - Best Known (246−59, 246, s)-Nets in Base 4

Best Known (246−59, 246, s)-Nets in Base 4

(246−59, 246, 1036)-Net over F₄ — Constructive and digital

Digital (187, 246, 1036)-net over F₄, using

4² times duplication [i] based on digital (185, 244, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 61, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(246−59, 246, 2706)-Net over F₄ — Digital

Digital (187, 246, 2706)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−59, 246, 474622)-Net in Base 4 — Upper bound on s

There is no (187, 246, 474623)-net in base 4, because

1 times m-reduction [i] would yield (187, 245, 474623)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3196 834676 885656 111483 265968 732831 150621 662492 172828 899706 197762 655467 744470 827486 452856 805792 979646 110524 182553 838889 232866 802103 688526 441798 282986 > 4²⁴⁵ [i]