MinT - Best Known (105, 105+47, s)-Nets in Base 4

Best Known (105, 105+47, s)-Nets in Base 4

(105, 105+47, 312)-Net over F₄ — Constructive and digital

Digital (105, 152, 312)-net over F₄, using

1 times m-reduction [i] based on digital (105, 153, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(105, 105+47, 584)-Net over F₄ — Digital

Digital (105, 152, 584)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+47, 28164)-Net in Base 4 — Upper bound on s

There is no (105, 152, 28165)-net in base 4, because

1 times m-reduction [i] would yield (105, 151, 28165)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 151454 254639 570470 497845 401463 137964 258683 412123 893056 419095 526024 821805 589217 149994 139136 > 4¹⁵¹ [i]