MinT - Best Known (162−62, 162, s)-Nets in Base 4

Best Known (162−62, 162, s)-Nets in Base 4

(162−62, 162, 130)-Net over F₄ — Constructive and digital

Digital (100, 162, 130)-net over F₄, using

26 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(162−62, 162, 283)-Net over F₄ — Digital

Digital (100, 162, 283)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−62, 162, 5771)-Net in Base 4 — Upper bound on s

There is no (100, 162, 5772)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 333254 952375 386419 253655 534423 239548 417970 737716 234082 975754 803415 273221 261776 914609 309903 895648 > 4¹⁶² [i]