MinT - Best Known (161−66, 161, s)-Nets in Base 4

Best Known (161−66, 161, s)-Nets in Base 4

(161−66, 161, 130)-Net over F₄ — Constructive and digital

Digital (95, 161, 130)-net over F₄, using

17 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(161−66, 161, 224)-Net over F₄ — Digital

Digital (95, 161, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−66, 161, 3771)-Net in Base 4 — Upper bound on s

There is no (95, 161, 3772)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 612423 965700 856639 004788 735001 221490 543911 630959 608415 483443 615332 780833 891166 126186 965132 535547 > 4¹⁶¹ [i]