MinT - Best Known (164−68, 164, s)-Nets in Base 4

Best Known (164−68, 164, s)-Nets in Base 4

(164−68, 164, 130)-Net over F₄ — Constructive and digital

Digital (96, 164, 130)-net over F₄, using

16 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(164−68, 164, 219)-Net over F₄ — Digital

Digital (96, 164, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−68, 164, 3589)-Net in Base 4 — Upper bound on s

There is no (96, 164, 3590)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 548 118852 498153 270080 351048 228299 546961 885592 428425 643276 565609 985284 338588 585718 302965 735432 364320 > 4¹⁶⁴ [i]