MinT - Best Known (178, 178+51, s)-Nets in Base 3

Best Known (178, 178+51, s)-Nets in Base 3

(178, 178+51, 640)-Net over F₃ — Constructive and digital

Digital (178, 229, 640)-net over F₃, using

3¹ times duplication [i] based on digital (177, 228, 640)-net over F₃, using
- t-expansion [i] based on digital (176, 228, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 57, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(178, 178+51, 1517)-Net over F₃ — Digital

Digital (178, 229, 1517)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+51, 114247)-Net in Base 3 — Upper bound on s

There is no (178, 229, 114248)-net in base 3, because

1 times m-reduction [i] would yield (178, 228, 114248)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 076412 150189 650862 024698 132591 165705 211122 383735 460415 237930 984735 528604 459165 214322 154962 658779 135193 197841 > 3²²⁸ [i]