MinT - Best Known (107, 107+41, s)-Nets in Base 3

Best Known (107, 107+41, s)-Nets in Base 3

(107, 107+41, 252)-Net over F₃ — Constructive and digital

Digital (107, 148, 252)-net over F₃, using

3¹ times duplication [i] based on digital (106, 147, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 49, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(107, 107+41, 452)-Net over F₃ — Digital

Digital (107, 148, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+41, 13319)-Net in Base 3 — Upper bound on s

There is no (107, 148, 13320)-net in base 3, because

1 times m-reduction [i] would yield (107, 147, 13320)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13716 981809 425377 310852 670668 547778 086363 384592 448104 491898 114999 125313 > 3¹⁴⁷ [i]