MinT - Best Known (131−55, 131, s)-Nets in Base 4

Best Known (131−55, 131, s)-Nets in Base 4

(131−55, 131, 130)-Net over F₄ — Constructive and digital

Digital (76, 131, 130)-net over F₄, using

9 times m-reduction [i] based on digital (76, 140, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 70, 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]

(131−55, 131, 174)-Net over F₄ — Digital

Digital (76, 131, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−55, 131, 2862)-Net in Base 4 — Upper bound on s

There is no (76, 131, 2863)-net in base 4, because

1 times m-reduction [i] would yield (76, 130, 2863)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 857661 968217 478954 711811 398212 256930 059422 892923 284862 219028 088559 842720 169088 > 4¹³⁰ [i]