MinT - Best Known (88, 88+70, s)-Nets in Base 4

Best Known (88, 88+70, s)-Nets in Base 4

(88, 88+70, 130)-Net over F₄ — Constructive and digital

Digital (88, 158, 130)-net over F₄, using

6 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+70, 172)-Net over F₄ — Digital

Digital (88, 158, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+70, 2392)-Net in Base 4 — Upper bound on s

There is no (88, 158, 2393)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134338 798566 422000 147244 097583 207773 228547 127069 292174 773211 882665 428930 527755 610129 980298 397200 > 4¹⁵⁸ [i]