MinT - Best Known (107, 107+47, s)-Nets in Base 4

Best Known (107, 107+47, s)-Nets in Base 4

(107, 107+47, 312)-Net over F₄ — Constructive and digital

Digital (107, 154, 312)-net over F₄, using

2 times m-reduction [i] based on digital (107, 156, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 52, 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]

(107, 107+47, 623)-Net over F₄ — Digital

Digital (107, 154, 623)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+47, 31775)-Net in Base 4 — Upper bound on s

There is no (107, 154, 31776)-net in base 4, because

1 times m-reduction [i] would yield (107, 153, 31776)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 449210 574528 053922 462085 708807 627682 375380 094947 485796 556054 698850 401250 991965 870979 790059 > 4¹⁵³ [i]