MinT - Best Known (158−54, 158, s)-Nets in Base 3

Best Known (158−54, 158, s)-Nets in Base 3

(158−54, 158, 156)-Net over F₃ — Constructive and digital

Digital (104, 158, 156)-net over F₃, using

6 times m-reduction [i] based on digital (104, 164, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 82, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(158−54, 158, 242)-Net over F₃ — Digital

Digital (104, 158, 242)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−54, 158, 3357)-Net in Base 3 — Upper bound on s

There is no (104, 158, 3358)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2437 136553 690387 279709 838600 069654 939606 070247 216970 487550 534703 061144 328337 > 3¹⁵⁸ [i]