MinT - Best Known (88, 88+73, s)-Nets in Base 4

Best Known (88, 88+73, s)-Nets in Base 4

(88, 88+73, 130)-Net over F₄ — Constructive and digital

Digital (88, 161, 130)-net over F₄, using

3 times m-reduction [i] based on digital (88, 164, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 82, 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]

(88, 88+73, 162)-Net over F₄ — Digital

Digital (88, 161, 162)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+73, 2227)-Net in Base 4 — Upper bound on s

There is no (88, 161, 2228)-net in base 4, because

1 times m-reduction [i] would yield (88, 160, 2228)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 164770 283079 288350 466371 067712 463319 800733 338604 222036 927800 859137 991378 849052 279838 899446 110300 > 4¹⁶⁰ [i]