MinT - Best Known (119, 181, s)-Nets in Base 4

Best Known (119, 181, s)-Nets in Base 4

(119, 181, 160)-Net over F₄ — Constructive and digital

Digital (119, 181, 160)-net over F₄, using

1 times m-reduction [i] based on digital (119, 182, 160)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 44, 30)-net over F₄, using
    - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
        F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (75, 138, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 69, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(119, 181, 208)-Net in Base 4 — Constructive

(119, 181, 208)-net in base 4, using

4¹ times duplication [i] based on (118, 180, 208)-net in base 4, using
- t-expansion [i] based on (117, 180, 208)-net in base 4, using
  - trace code for nets [i] based on (27, 90, 104)-net in base 16, using
    - base change [i] based on digital (9, 72, 104)-net over F₃₂, using
      - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(119, 181, 457)-Net over F₄ — Digital

Digital (119, 181, 457)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 181, 13531)-Net in Base 4 — Upper bound on s

There is no (119, 181, 13532)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 399864 134152 514893 663202 608480 418846 537189 653826 697952 833950 881299 197449 608618 716214 853914 267447 874865 218288 > 4¹⁸¹ [i]