MinT - Best Known (172−68, 172, s)-Nets in Base 4

Best Known (172−68, 172, s)-Nets in Base 4

(172−68, 172, 130)-Net over F₄ — Constructive and digital

Digital (104, 172, 130)-net over F₄, using

24 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(172−68, 172, 267)-Net over F₄ — Digital

Digital (104, 172, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−68, 172, 4984)-Net in Base 4 — Upper bound on s

There is no (104, 172, 4985)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 860372 990938 626774 460428 736067 673142 974947 419385 291220 013723 344167 316269 064142 592078 248840 835618 453492 > 4¹⁷² [i]