MinT - Best Known (150−66, 150, s)-Nets in Base 3

Best Known (150−66, 150, s)-Nets in Base 3

(150−66, 150, 80)-Net over F₃ — Constructive and digital

Digital (84, 150, 80)-net over F₃, using

2 times m-reduction [i] based on digital (84, 152, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 76, 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]

(150−66, 150, 112)-Net over F₃ — Digital

Digital (84, 150, 112)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−66, 150, 938)-Net in Base 3 — Upper bound on s

There is no (84, 150, 939)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 375261 959391 105241 985949 004096 079213 201012 045777 081485 695028 906217 961495 > 3¹⁵⁰ [i]