MinT - Best Known (164−65, 164, s)-Nets in Base 4

Best Known (164−65, 164, s)-Nets in Base 4

(164−65, 164, 130)-Net over F₄ — Constructive and digital

Digital (99, 164, 130)-net over F₄, using

22 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(164−65, 164, 254)-Net over F₄ — Digital

Digital (99, 164, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−65, 164, 4945)-Net in Base 4 — Upper bound on s

There is no (99, 164, 4946)-net in base 4, because

1 times m-reduction [i] would yield (99, 163, 4946)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 137 095317 306111 277348 659048 501640 750497 527695 393247 747544 663205 224424 675416 173869 411119 673263 106570 > 4¹⁶³ [i]