MinT - Best Known (178−78, 178, s)-Nets in Base 3

Best Known (178−78, 178, s)-Nets in Base 3

(178−78, 178, 80)-Net over F₃ — Constructive and digital

Digital (100, 178, 80)-net over F₃, using

6 times m-reduction [i] based on digital (100, 184, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 92, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(178−78, 178, 131)-Net over F₃ — Digital

Digital (100, 178, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−78, 178, 1120)-Net in Base 3 — Upper bound on s

There is no (100, 178, 1121)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 501272 381644 039236 344259 705060 148928 553455 263834 098102 770768 821428 011321 949784 897931 > 3¹⁷⁸ [i]