MinT - Best Known (161−65, 161, s)-Nets in Base 4

Best Known (161−65, 161, s)-Nets in Base 4

(161−65, 161, 130)-Net over F₄ — Constructive and digital

Digital (96, 161, 130)-net over F₄, using

19 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]

(161−65, 161, 235)-Net over F₄ — Digital

Digital (96, 161, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−65, 161, 4339)-Net in Base 4 — Upper bound on s

There is no (96, 161, 4340)-net in base 4, because

1 times m-reduction [i] would yield (96, 160, 4340)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 141544 683927 343709 854188 061768 762606 051874 809600 749495 053189 510855 368085 260829 712279 756108 979325 > 4¹⁶⁰ [i]