MinT - Best Known (170−70, 170, s)-Nets in Base 4

Best Known (170−70, 170, s)-Nets in Base 4

(170−70, 170, 130)-Net over F₄ — Constructive and digital

Digital (100, 170, 130)-net over F₄, using

18 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]

(170−70, 170, 231)-Net over F₄ — Digital

Digital (100, 170, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−70, 170, 3865)-Net in Base 4 — Upper bound on s

There is no (100, 170, 3866)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 244691 509499 121373 095816 759356 948590 655705 373985 582415 805367 353176 314355 762424 227511 691271 104595 514080 > 4¹⁷⁰ [i]