MinT - Best Known (164−70, 164, s)-Nets in Base 4

Best Known (164−70, 164, s)-Nets in Base 4

(164−70, 164, 130)-Net over F₄ — Constructive and digital

Digital (94, 164, 130)-net over F₄, using

12 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(164−70, 164, 200)-Net over F₄ — Digital

Digital (94, 164, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−70, 164, 3042)-Net in Base 4 — Upper bound on s

There is no (94, 164, 3043)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 552 838831 449777 707695 292568 425370 584369 636895 828058 580545 723379 036638 888370 820561 043143 488835 842980 > 4¹⁶⁴ [i]