MinT - Best Known (170−77, 170, s)-Nets in Base 4

Best Known (170−77, 170, s)-Nets in Base 4

(170−77, 170, 130)-Net over F₄ — Constructive and digital

Digital (93, 170, 130)-net over F₄, using

4 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(170−77, 170, 170)-Net over F₄ — Digital

Digital (93, 170, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−77, 170, 2352)-Net in Base 4 — Upper bound on s

There is no (93, 170, 2353)-net in base 4, because

1 times m-reduction [i] would yield (93, 169, 2353)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 562087 827655 734689 319764 649250 821668 974450 878488 444000 285829 471732 610147 421692 519318 435392 728700 001720 > 4¹⁶⁹ [i]