MinT - Best Known (189−44, 189, s)-Nets in Base 4

Best Known (189−44, 189, s)-Nets in Base 4

(189−44, 189, 1040)-Net over F₄ — Constructive and digital

Digital (145, 189, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (144, 188, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 47, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(189−44, 189, 2514)-Net over F₄ — Digital

Digital (145, 189, 2514)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−44, 189, 448701)-Net in Base 4 — Upper bound on s

There is no (145, 189, 448702)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615682 558578 458757 356171 631831 653795 893160 153073 144814 741825 139568 369874 425518 761272 317318 853729 740898 748827 343180 > 4¹⁸⁹ [i]