MinT - Best Known (160−62, 160, s)-Nets in Base 4

Best Known (160−62, 160, s)-Nets in Base 4

(160−62, 160, 130)-Net over F₄ — Constructive and digital

Digital (98, 160, 130)-net over F₄, using

24 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(160−62, 160, 269)-Net over F₄ — Digital

Digital (98, 160, 269)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−62, 160, 5275)-Net in Base 4 — Upper bound on s

There is no (98, 160, 5276)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 145644 380696 518161 502297 606310 202879 678846 760668 052985 675256 188035 697589 199206 074750 901949 724192 > 4¹⁶⁰ [i]