MinT - Best Known (152, 233, s)-Nets in Base 4

Best Known (152, 233, s)-Nets in Base 4

(152, 233, 163)-Net over F₄ — Constructive and digital

Digital (152, 233, 163)-net over F₄, using

t-expansion [i] based on digital (151, 233, 163)-net over F₄, using
- 1 times m-reduction [i] based on digital (151, 234, 163)-net over F₄, using
  - (u,Â u+v)-construction [i] based on
    1. digital (15, 56, 33)-net over F₄, using
      - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
    2. digital (95, 178, 130)-net over F₄, using
      - trace code for nets [i] based on digital (6, 89, 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]

(152, 233, 240)-Net in Base 4 — Constructive

(152, 233, 240)-net in base 4, using

1 times m-reduction [i] based on (152, 234, 240)-net in base 4, using
- trace code for nets [i] based on (35, 117, 120)-net in base 16, using
  - 3 times m-reduction [i] based on (35, 120, 120)-net in base 16, using
    - base change [i] based on digital (11, 96, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(152, 233, 542)-Net over F₄ — Digital

Digital (152, 233, 542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 233, 16283)-Net in Base 4 — Upper bound on s

There is no (152, 233, 16284)-net in base 4, because

1 times m-reduction [i] would yield (152, 232, 16284)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 710424 753185 590400 224936 569632 444112 112579 696114 898302 792032 028829 819122 367374 155483 448327 961841 660590 699474 083876 665542 560413 734273 138516 > 4²³² [i]