MinT - Best Known (23−8, 23, s)-Nets in Base 4

Best Known (23−8, 23, s)-Nets in Base 4

(23−8, 23, 76)-Net over F₄ — Constructive and digital

Digital (15, 23, 76)-net over F₄, using

1 times m-reduction [i] based on digital (15, 24, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 12, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(23−8, 23, 143)-Net over F₄ — Digital

Digital (15, 23, 143)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²³, 143, F₄, 8) (dual of [143, 120, 9]-code), using
- 1 times truncation [i] based on linear OA(4²⁴, 144, F₄, 9) (dual of [144, 120, 10]-code), using
  - a code from Grasslâ€™s database [i]

(23−8, 23, 2134)-Net in Base 4 — Upper bound on s

There is no (15, 23, 2135)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 70 496556 523891 > 4²³ [i]