MinT - Best Known (138−52, 138, s)-Nets in Base 4

Best Known (138−52, 138, s)-Nets in Base 4

(138−52, 138, 130)-Net over F₄ — Constructive and digital

Digital (86, 138, 130)-net over F₄, using

22 times m-reduction [i] based on digital (86, 160, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 80, 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]

(138−52, 138, 261)-Net over F₄ — Digital

Digital (86, 138, 261)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−52, 138, 5496)-Net in Base 4 — Upper bound on s

There is no (86, 138, 5497)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 121936 824597 460000 091039 030327 507434 331122 744583 045354 420703 294044 583912 586281 562912 > 4¹³⁸ [i]