MinT - Best Known (194−47, 194, s)-Nets in Base 4

Best Known (194−47, 194, s)-Nets in Base 4

(194−47, 194, 1032)-Net over F₄ — Constructive and digital

Digital (147, 194, 1032)-net over F₄, using

4² times duplication [i] based on digital (145, 192, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 48, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(194−47, 194, 2099)-Net over F₄ — Digital

Digital (147, 194, 2099)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−47, 194, 354307)-Net in Base 4 — Upper bound on s

There is no (147, 194, 354308)-net in base 4, because

1 times m-reduction [i] would yield (147, 193, 354308)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 157 609614 793032 125368 189025 657123 247629 157861 440994 646195 625692 801706 770779 386763 352564 020532 403793 217711 121242 478080 > 4¹⁹³ [i]