MinT - Best Known (184, 184+68, s)-Nets in Base 4

Best Known (184, 184+68, s)-Nets in Base 4

(184, 184+68, 531)-Net over F₄ — Constructive and digital

Digital (184, 252, 531)-net over F₄, using

t-expansion [i] based on digital (179, 252, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(184, 184+68, 576)-Net in Base 4 — Constructive

(184, 252, 576)-net in base 4, using

t-expansion [i] based on (183, 252, 576)-net in base 4, using
- trace code for nets [i] based on (15, 84, 192)-net in base 64, using
  - base change [i] based on digital (3, 72, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(184, 184+68, 1601)-Net over F₄ — Digital

Digital (184, 252, 1601)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184, 184+68, 130794)-Net in Base 4 — Upper bound on s

There is no (184, 252, 130795)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 383984 058371 829384 255026 590428 698100 856550 535694 076033 532973 349271 413456 093941 219527 810498 955645 819384 455631 267801 741452 805352 836831 585181 559889 676571 > 4²⁵² [i]