MinT - Best Known (187−83, 187, s)-Nets in Base 4

Best Known (187−83, 187, s)-Nets in Base 4

(187−83, 187, 130)-Net over F₄ — Constructive and digital

Digital (104, 187, 130)-net over F₄, using

9 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]

(187−83, 187, 197)-Net over F₄ — Digital

Digital (104, 187, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−83, 187, 2864)-Net in Base 4 — Upper bound on s

There is no (104, 187, 2865)-net in base 4, because

1 times m-reduction [i] would yield (104, 186, 2865)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9699 666780 280916 520517 088923 691763 879299 450277 271018 250503 902484 028539 894710 578540 420608 309367 449423 846777 409080 > 4¹⁸⁶ [i]