MinT - Best Known (242−42, 242, s)-Nets in Base 4

Best Known (242−42, 242, s)-Nets in Base 4

(242−42, 242, 1566)-Net over F₄ — Constructive and digital

Digital (200, 242, 1566)-net over F₄, using

4¹ times duplication [i] based on digital (199, 241, 1566)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 31, 27)-net over F₄, using
    - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
        an explicitly constructive algebraic function field [i]
  2. digital (168, 210, 1539)-net over F₄, using
    - trace code for nets [i] based on digital (28, 70, 513)-net over F₆₄, using
      - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(242−42, 242, 19269)-Net over F₄ — Digital

Digital (200, 242, 19269)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−42, 242, large)-Net in Base 4 — Upper bound on s

There is no (200, 242, large)-net in base 4, because

40 times m-reduction [i] would yield (200, 202, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]