MinT - Best Known (106, 106+45, s)-Nets in Base 4

Best Known (106, 106+45, s)-Nets in Base 4

(106, 106+45, 384)-Net over F₄ — Constructive and digital

Digital (106, 151, 384)-net over F₄, using

4¹ times duplication [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+45, 678)-Net over F₄ — Digital

Digital (106, 151, 678)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+45, 38413)-Net in Base 4 — Upper bound on s

There is no (106, 151, 38414)-net in base 4, because

1 times m-reduction [i] would yield (106, 150, 38414)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 037532 142360 641778 573808 073446 328734 314938 254741 690854 146080 611096 525416 914281 203511 113600 > 4¹⁵⁰ [i]