MinT - Best Known (174−78, 174, s)-Nets in Base 4

Best Known (174−78, 174, s)-Nets in Base 4

(174−78, 174, 130)-Net over F₄ — Constructive and digital

Digital (96, 174, 130)-net over F₄, using

6 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]

(174−78, 174, 180)-Net over F₄ — Digital

Digital (96, 174, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−78, 174, 2459)-Net in Base 4 — Upper bound on s

There is no (96, 174, 2460)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 578 700143 280006 220431 996520 425667 920500 026076 285790 633108 302579 603333 938508 143602 718935 041861 922068 111800 > 4¹⁷⁴ [i]