MinT - Best Known (177−81, 177, s)-Nets in Base 4

Best Known (177−81, 177, s)-Nets in Base 4

(177−81, 177, 130)-Net over F₄ — Constructive and digital

Digital (96, 177, 130)-net over F₄, using

3 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(177−81, 177, 171)-Net over F₄ — Digital

Digital (96, 177, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−81, 177, 2310)-Net in Base 4 — Upper bound on s

There is no (96, 177, 2311)-net in base 4, because

1 times m-reduction [i] would yield (96, 176, 2311)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9310 582651 489069 821463 132128 322678 118149 760032 897428 493071 412949 627871 560604 933742 354626 704497 955103 279520 > 4¹⁷⁶ [i]