MinT - Best Known (152, 152+82, s)-Nets in Base 4

Best Known (152, 152+82, s)-Nets in Base 4

(152, 152+82, 163)-Net over F₄ — Constructive and digital

Digital (152, 234, 163)-net over F₄, using

t-expansion [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, 152+82, 240)-Net in Base 4 — Constructive

(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, 152+82, 529)-Net over F₄ — Digital

Digital (152, 234, 529)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+82, 14653)-Net in Base 4 — Upper bound on s

There is no (152, 234, 14654)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 763 083076 123795 538932 951899 397018 292527 300254 203235 850483 241460 834544 018098 577511 717339 709288 983328 269607 326397 013184 037225 938610 419712 521629 > 4²³⁴ [i]