MinT - Best Known (182−81, 182, s)-Nets in Base 4

Best Known (182−81, 182, s)-Nets in Base 4

(182−81, 182, 130)-Net over F₄ — Constructive and digital

Digital (101, 182, 130)-net over F₄, using

8 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(182−81, 182, 191)-Net over F₄ — Digital

Digital (101, 182, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−81, 182, 2753)-Net in Base 4 — Upper bound on s

There is no (101, 182, 2754)-net in base 4, because

1 times m-reduction [i] would yield (101, 181, 2754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 478208 896604 212608 090138 764007 341319 109481 291213 660923 249021 711675 539202 184172 140647 842815 467673 456066 694136 > 4¹⁸¹ [i]