MinT - Best Known (186, 241, s)-Nets in Base 4

Best Known (186, 241, s)-Nets in Base 4

(186, 241, 1048)-Net over F₄ — Constructive and digital

Digital (186, 241, 1048)-net over F₄, using

4¹ times duplication [i] based on digital (185, 240, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 60, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(186, 241, 3426)-Net over F₄ — Digital

Digital (186, 241, 3426)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 241, 818310)-Net in Base 4 — Upper bound on s

There is no (186, 241, 818311)-net in base 4, because

1 times m-reduction [i] would yield (186, 240, 818311)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 121783 880693 621921 847254 929817 579396 974087 238359 884746 829319 613905 347117 233710 502946 720889 727368 679145 089990 837286 561304 475591 022709 767105 535360 > 4²⁴⁰ [i]