MinT - Best Known (88, 88+57, s)-Nets in Base 4

Best Known (88, 88+57, s)-Nets in Base 4

(88, 88+57, 130)-Net over F₄ — Constructive and digital

Digital (88, 145, 130)-net over F₄, using

19 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+57, 236)-Net over F₄ — Digital

Digital (88, 145, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+57, 4678)-Net in Base 4 — Upper bound on s

There is no (88, 145, 4679)-net in base 4, because

1 times m-reduction [i] would yield (88, 144, 4679)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 499 604902 347405 180092 686780 400948 140927 625071 408122 718321 178245 592805 070956 296410 604680 > 4¹⁴⁴ [i]