MinT - Best Known (106, 106+43, s)-Nets in Base 4

Best Known (106, 106+43, s)-Nets in Base 4

(106, 106+43, 384)-Net over F₄ — Constructive and digital

Digital (106, 149, 384)-net over F₄, using

t-expansion [i] based on digital (105, 149, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (105, 150, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 50, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(106, 106+43, 772)-Net over F₄ — Digital

Digital (106, 149, 772)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+43, 50619)-Net in Base 4 — Upper bound on s

There is no (106, 149, 50620)-net in base 4, because

1 times m-reduction [i] would yield (106, 148, 50620)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127358 919620 338578 929634 014413 276422 752623 676434 969236 177857 810021 384787 777642 391097 110354 > 4¹⁴⁸ [i]