MinT - Best Known (243−93, 243, s)-Nets in Base 3

Best Known (243−93, 243, s)-Nets in Base 3

(243−93, 243, 156)-Net over F₃ — Constructive and digital

Digital (150, 243, 156)-net over F₃, using

t-expansion [i] based on digital (147, 243, 156)-net over F₃, using
- 7 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(243−93, 243, 251)-Net over F₃ — Digital

Digital (150, 243, 251)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−93, 243, 2867)-Net in Base 3 — Upper bound on s

There is no (150, 243, 2868)-net in base 3, because

1 times m-reduction [i] would yield (150, 242, 2868)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 368695 240237 395125 649950 170292 215968 808283 993716 723124 148296 675543 859032 134443 950545 907053 291768 336202 144880 800761 > 3²⁴² [i]