MinT - Best Known (84, 84+64, s)-Nets in Base 4

Best Known (84, 84+64, s)-Nets in Base 4

(84, 84+64, 130)-Net over F₄ — Constructive and digital

Digital (84, 148, 130)-net over F₄, using

8 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(84, 84+64, 175)-Net over F₄ — Digital

Digital (84, 148, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+64, 2569)-Net in Base 4 — Upper bound on s

There is no (84, 148, 2570)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127588 362313 435201 720026 246839 133324 709439 713371 696649 688971 649611 223013 484204 462184 796400 > 4¹⁴⁸ [i]