MinT - Best Known (177−76, 177, s)-Nets in Base 3

Best Known (177−76, 177, s)-Nets in Base 3

(177−76, 177, 80)-Net over F₃ — Constructive and digital

Digital (101, 177, 80)-net over F₃, using

9 times m-reduction [i] based on digital (101, 186, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 93, 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]

(177−76, 177, 138)-Net over F₃ — Digital

Digital (101, 177, 138)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−76, 177, 1216)-Net in Base 3 — Upper bound on s

There is no (101, 177, 1217)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 860517 966385 409494 101452 497344 887141 616288 307980 282050 291002 971297 013529 146272 623833 > 3¹⁷⁷ [i]