MinT - Best Known (168, 168+60, s)-Nets in Base 4

Best Known (168, 168+60, s)-Nets in Base 4

(168, 168+60, 531)-Net over F₄ — Constructive and digital

Digital (168, 228, 531)-net over F₄, using

t-expansion [i] based on digital (167, 228, 531)-net over F₄, using
- 12 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 80, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(168, 168+60, 648)-Net in Base 4 — Constructive

(168, 228, 648)-net in base 4, using

trace code for nets [i] based on (16, 76, 216)-net in base 64, using
- 1 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(168, 168+60, 1643)-Net over F₄ — Digital

Digital (168, 228, 1643)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+60, 151095)-Net in Base 4 — Upper bound on s

There is no (168, 228, 151096)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186071 084946 136692 220200 553240 318066 009240 248627 119358 491296 906912 244054 109232 063510 887241 493180 699941 840959 308306 768653 416602 354397 762028 > 4²²⁸ [i]