MinT - Best Known (145, 145+97, s)-Nets in Base 3

Best Known (145, 145+97, s)-Nets in Base 3

(145, 145+97, 156)-Net over F₃ — Constructive and digital

Digital (145, 242, 156)-net over F₃, using

4 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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]

(145, 145+97, 219)-Net over F₃ — Digital

Digital (145, 242, 219)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+97, 2282)-Net in Base 3 — Upper bound on s

There is no (145, 242, 2283)-net in base 3, because

1 times m-reduction [i] would yield (145, 241, 2283)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 761435 777277 143702 563904 234052 158420 258289 761891 049616 294285 236568 250144 950750 332169 271874 808513 549677 825220 397985 > 3²⁴¹ [i]