MinT - Best Known (152, 152+85, s)-Nets in Base 4

Best Known (152, 152+85, s)-Nets in Base 4

(152, 152+85, 160)-Net over F₄ — Constructive and digital

Digital (152, 237, 160)-net over F₄, using

7 times m-reduction [i] based on digital (152, 244, 160)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (33, 79, 56)-net over F₄, using
    - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
        F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 165, 104)-net over F₄, using
    - net from sequence [i] based on digital (73, 103)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
        F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(152, 152+85, 208)-Net in Base 4 — Constructive

(152, 237, 208)-net in base 4, using

1 times m-reduction [i] based on (152, 238, 208)-net in base 4, using
- trace code for nets [i] based on (33, 119, 104)-net in base 16, using
  - 1 times m-reduction [i] based on (33, 120, 104)-net in base 16, using
    - base change [i] based on digital (9, 96, 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]

(152, 152+85, 493)-Net over F₄ — Digital

Digital (152, 237, 493)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+85, 13260)-Net in Base 4 — Upper bound on s

There is no (152, 237, 13261)-net in base 4, because

1 times m-reduction [i] would yield (152, 236, 13261)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12216 978389 905679 890580 400843 655659 332169 269792 691952 705657 379665 309680 256238 309929 498201 303301 458461 793395 289207 698761 827670 419445 112349 185220 > 4²³⁶ [i]