MinT - Best Known (180−82, 180, s)-Nets in Base 4

Best Known (180−82, 180, s)-Nets in Base 4

(180−82, 180, 130)-Net over F₄ — Constructive and digital

Digital (98, 180, 130)-net over F₄, using

4 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(180−82, 180, 176)-Net over F₄ — Digital

Digital (98, 180, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−82, 180, 2332)-Net in Base 4 — Upper bound on s

There is no (98, 180, 2333)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 375705 319951 630087 834810 377621 381520 869852 801373 928298 277396 107123 167898 703704 640660 280415 037907 656855 097600 > 4¹⁸⁰ [i]