MinT - Best Known (137, 171, s)-Nets in Base 4

Best Known (137, 171, s)-Nets in Base 4

(137, 171, 1064)-Net over F₄ — Constructive and digital

Digital (137, 171, 1064)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (14, 31, 32)-net over F₄, using
  - 1 times m-reduction [i] based on digital (14, 32, 32)-net over F₄, using
    - a shift-net [i]
2. digital (106, 140, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 35, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(137, 171, 5797)-Net over F₄ — Digital

Digital (137, 171, 5797)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 171, 2721679)-Net in Base 4 — Upper bound on s

There is no (137, 171, 2721680)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 959008 341628 151484 670932 072111 333320 496266 848824 499297 376423 246730 618510 586952 737113 779003 167488 908024 > 4¹⁷¹ [i]