MinT - Best Known (180−76, 180, s)-Nets in Base 4

Best Known (180−76, 180, s)-Nets in Base 4

(180−76, 180, 130)-Net over F₄ — Constructive and digital

Digital (104, 180, 130)-net over F₄, using

16 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(180−76, 180, 224)-Net over F₄ — Digital

Digital (104, 180, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−76, 180, 3529)-Net in Base 4 — Upper bound on s

There is no (104, 180, 3530)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 355656 746793 002583 567666 764029 016032 505908 129368 684562 044765 957637 804123 668693 440394 193497 519898 901532 096872 > 4¹⁸⁰ [i]