MinT - Best Known (88, 88+64, s)-Nets in Base 4

Best Known (88, 88+64, s)-Nets in Base 4

(88, 88+64, 130)-Net over F₄ — Constructive and digital

Digital (88, 152, 130)-net over F₄, using

12 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+64, 195)-Net over F₄ — Digital

Digital (88, 152, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+64, 3060)-Net in Base 4 — Upper bound on s

There is no (88, 152, 3061)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 602353 168430 065375 963997 016398 836187 404327 861356 766871 815881 315003 829675 638092 504380 752605 > 4¹⁵² [i]