MinT - Best Known (191−45, 191, s)-Nets in Base 4

Best Known (191−45, 191, s)-Nets in Base 4

(191−45, 191, 1036)-Net over F₄ — Constructive and digital

Digital (146, 191, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (146, 192, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 48, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(191−45, 191, 2384)-Net over F₄ — Digital

Digital (146, 191, 2384)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−45, 191, 477886)-Net in Base 4 — Upper bound on s

There is no (146, 191, 477887)-net in base 4, because

1 times m-reduction [i] would yield (146, 190, 477887)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 462704 524543 213861 394489 479583 523702 378360 679067 446971 559199 871838 350496 832877 289806 482835 706790 685057 166751 498195 > 4¹⁹⁰ [i]