MinT - Best Known (186−83, 186, s)-Nets in Base 4

Best Known (186−83, 186, s)-Nets in Base 4

(186−83, 186, 130)-Net over F₄ — Constructive and digital

Digital (103, 186, 130)-net over F₄, using

8 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(186−83, 186, 193)-Net over F₄ — Digital

Digital (103, 186, 193)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−83, 186, 2768)-Net in Base 4 — Upper bound on s

There is no (103, 186, 2769)-net in base 4, because

1 times m-reduction [i] would yield (103, 185, 2769)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2437 773249 373408 274819 042360 891302 556579 219341 700011 574471 307411 898380 033107 080853 532296 506554 653634 138290 971024 > 4¹⁸⁵ [i]