MinT - Best Known (163−67, 163, s)-Nets in Base 4

Best Known (163−67, 163, s)-Nets in Base 4

(163−67, 163, 130)-Net over F₄ — Constructive and digital

Digital (96, 163, 130)-net over F₄, using

17 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]

(163−67, 163, 224)-Net over F₄ — Digital

Digital (96, 163, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−67, 163, 3934)-Net in Base 4 — Upper bound on s

There is no (96, 163, 3935)-net in base 4, because

1 times m-reduction [i] would yield (96, 162, 3935)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 453912 618220 048678 951007 385080 901829 111623 228683 205457 954846 650059 571117 552732 886061 524074 043260 > 4¹⁶² [i]