MinT - Best Known (69, 111, s)-Nets in Base 4

Best Known (69, 111, s)-Nets in Base 4

(69, 111, 130)-Net over F₄ — Constructive and digital

Digital (69, 111, 130)-net over F₄, using

15 times m-reduction [i] based on digital (69, 126, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 63, 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]

(69, 111, 215)-Net over F₄ — Digital

Digital (69, 111, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 111, 4385)-Net in Base 4 — Upper bound on s

There is no (69, 111, 4386)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 758843 707733 737941 356519 264313 642057 024831 963040 802204 306531 606104 > 4¹¹¹ [i]