MinT - Best Known (188−87, 188, s)-Nets in Base 4

Best Known (188−87, 188, s)-Nets in Base 4

(188−87, 188, 130)-Net over F₄ — Constructive and digital

Digital (101, 188, 130)-net over F₄, using

2 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(188−87, 188, 174)-Net over F₄ — Digital

Digital (101, 188, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−87, 188, 2301)-Net in Base 4 — Upper bound on s

There is no (101, 188, 2302)-net in base 4, because

1 times m-reduction [i] would yield (101, 187, 2302)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38764 414221 199495 818168 014457 431881 559873 922661 020907 660343 630057 595868 837191 562073 238960 186744 410480 280592 558510 > 4¹⁸⁷ [i]