MinT - Best Known (172−71, 172, s)-Nets in Base 4

Best Known (172−71, 172, s)-Nets in Base 4

(172−71, 172, 130)-Net over F₄ — Constructive and digital

Digital (101, 172, 130)-net over F₄, using

18 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(172−71, 172, 231)-Net over F₄ — Digital

Digital (101, 172, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−71, 172, 4023)-Net in Base 4 — Upper bound on s

There is no (101, 172, 4024)-net in base 4, because

1 times m-reduction [i] would yield (101, 171, 4024)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 029243 597490 172690 190808 017346 320525 035570 286516 396941 730557 636304 050496 284109 706487 645268 904555 027919 > 4¹⁷¹ [i]