MinT - Best Known (140, 140+35, s)-Nets in Base 4

Best Known (140, 140+35, s)-Nets in Base 4

(140, 140+35, 1064)-Net over F₄ — Constructive and digital

Digital (140, 175, 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 (109, 144, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(140, 140+35, 5682)-Net over F₄ — Digital

Digital (140, 175, 5682)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+35, 3476028)-Net in Base 4 — Upper bound on s

There is no (140, 175, 3476029)-net in base 4, because

1 times m-reduction [i] would yield (140, 174, 3476029)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 375973 444043 452136 532907 844713 986738 689353 280926 809900 263799 423469 811150 813724 211613 374125 804960 870760 > 4¹⁷⁴ [i]