MinT - Best Known (85, 85+69, s)-Nets in Base 4

Best Known (85, 85+69, s)-Nets in Base 4

(85, 85+69, 130)-Net over F₄ — Constructive and digital

Digital (85, 154, 130)-net over F₄, using

4 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 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]

(85, 85+69, 162)-Net over F₄ — Digital

Digital (85, 154, 162)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+69, 2282)-Net in Base 4 — Upper bound on s

There is no (85, 154, 2283)-net in base 4, because

1 times m-reduction [i] would yield (85, 153, 2283)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 131 605458 550154 662142 805160 525080 431469 803460 874894 189180 289562 350810 842810 579165 363506 443659 > 4¹⁵³ [i]