MinT - Best Known (163−73, 163, s)-Nets in Base 4

Best Known (163−73, 163, s)-Nets in Base 4

(163−73, 163, 130)-Net over F₄ — Constructive and digital

Digital (90, 163, 130)-net over F₄, using

5 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(163−73, 163, 170)-Net over F₄ — Digital

Digital (90, 163, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−73, 163, 2407)-Net in Base 4 — Upper bound on s

There is no (90, 163, 2408)-net in base 4, because

1 times m-reduction [i] would yield (90, 162, 2408)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 273879 914764 101920 568758 758016 963480 315323 473460 793138 917061 195293 502148 305082 250859 430293 739765 > 4¹⁶² [i]