MinT - Best Known (83, 83+62, s)-Nets in Base 4

Best Known (83, 83+62, s)-Nets in Base 4

(83, 83+62, 130)-Net over F₄ — Constructive and digital

Digital (83, 145, 130)-net over F₄, using

9 times m-reduction [i] based on digital (83, 154, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 77, 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]

(83, 83+62, 179)-Net over F₄ — Digital

Digital (83, 145, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+62, 2684)-Net in Base 4 — Upper bound on s

There is no (83, 145, 2685)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1990 632810 754102 844970 419320 736926 999898 246758 523675 623734 771999 403794 122457 584821 272160 > 4¹⁴⁵ [i]