MinT - Best Known (86, 149, s)-Nets in Base 4

Best Known (86, 149, s)-Nets in Base 4

(86, 149, 130)-Net over F₄ — Constructive and digital

Digital (86, 149, 130)-net over F₄, using

11 times m-reduction [i] based on digital (86, 160, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 80, 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]

(86, 149, 189)-Net over F₄ — Digital

Digital (86, 149, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 149, 3074)-Net in Base 4 — Upper bound on s

There is no (86, 149, 3075)-net in base 4, because

1 times m-reduction [i] would yield (86, 148, 3075)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 128544 409371 594239 924370 026121 995245 744058 561855 078759 199272 932108 493686 579512 390424 145920 > 4¹⁴⁸ [i]