MinT - Best Known (186, 186+54, s)-Nets in Base 4

Best Known (186, 186+54, s)-Nets in Base 4

(186, 186+54, 1052)-Net over F₄ — Constructive and digital

Digital (186, 240, 1052)-net over F₄, using

trace code for nets [i] based on digital (6, 60, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(186, 186+54, 3682)-Net over F₄ — Digital

Digital (186, 240, 3682)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+54, 818310)-Net in Base 4 — Upper bound on s

There is no (186, 240, 818311)-net in base 4, because

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]