MinT - Best Known (189−43, 189, s)-Nets in Base 4

Best Known (189−43, 189, s)-Nets in Base 4

(189−43, 189, 1044)-Net over F₄ — Constructive and digital

Digital (146, 189, 1044)-net over F₄, using

4¹ times duplication [i] based on digital (145, 188, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 47, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(189−43, 189, 2839)-Net over F₄ — Digital

Digital (146, 189, 2839)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−43, 189, 709955)-Net in Base 4 — Upper bound on s

There is no (146, 189, 709956)-net in base 4, because

1 times m-reduction [i] would yield (146, 188, 709956)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153914 993414 467503 535319 233158 098414 469940 605219 908604 573047 529304 553658 339333 491466 835747 906486 649936 325423 260176 > 4¹⁸⁸ [i]