MinT - Best Known (152, 152+56, s)-Nets in Base 4

Best Known (152, 152+56, s)-Nets in Base 4

(152, 152+56, 531)-Net over F₄ — Constructive and digital

Digital (152, 208, 531)-net over F₄, using

t-expansion [i] based on digital (151, 208, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(152, 152+56, 576)-Net in Base 4 — Constructive

(152, 208, 576)-net in base 4, using

4¹ times duplication [i] based on (151, 207, 576)-net in base 4, using
- trace code for nets [i] based on (13, 69, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
    - base change [i] based on digital (3, 60, 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]

(152, 152+56, 1373)-Net over F₄ — Digital

Digital (152, 208, 1373)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+56, 111748)-Net in Base 4 — Upper bound on s

There is no (152, 208, 111749)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169262 441214 789908 507441 810753 612607 981164 966035 114398 735506 237210 862238 223245 801756 167522 212501 191675 798915 523439 271557 264112 > 4²⁰⁸ [i]