MinT - Best Known (169−65, 169, s)-Nets in Base 4

Best Known (169−65, 169, s)-Nets in Base 4

(169−65, 169, 130)-Net over F₄ — Constructive and digital

Digital (104, 169, 130)-net over F₄, using

27 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]

(169−65, 169, 288)-Net over F₄ — Digital

Digital (104, 169, 288)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−65, 169, 6147)-Net in Base 4 — Upper bound on s

There is no (104, 169, 6148)-net in base 4, because

1 times m-reduction [i] would yield (104, 168, 6148)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 139997 368387 008682 156588 320320 517203 553439 259154 404597 600804 462892 622457 860443 890335 266392 330740 716352 > 4¹⁶⁸ [i]