MinT - Best Known (105, 105+43, s)-Nets in Base 3

Best Known (105, 105+43, s)-Nets in Base 3

(105, 105+43, 228)-Net over F₃ — Constructive and digital

Digital (105, 148, 228)-net over F₃, using

3¹ times duplication [i] based on digital (104, 147, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 49, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(105, 105+43, 383)-Net over F₃ — Digital

Digital (105, 148, 383)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+43, 9470)-Net in Base 3 — Upper bound on s

There is no (105, 148, 9471)-net in base 3, because

1 times m-reduction [i] would yield (105, 147, 9471)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13718 294169 122579 973104 383208 336169 242240 598501 344495 766329 397066 719703 > 3¹⁴⁷ [i]