MinT - Best Known (242−91, 242, s)-Nets in Base 3

Best Known (242−91, 242, s)-Nets in Base 3

(242−91, 242, 156)-Net over F₃ — Constructive and digital

Digital (151, 242, 156)-net over F₃, using

t-expansion [i] based on digital (147, 242, 156)-net over F₃, using
- 8 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]

(242−91, 242, 263)-Net over F₃ — Digital

Digital (151, 242, 263)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−91, 242, 3120)-Net in Base 3 — Upper bound on s

There is no (151, 242, 3121)-net in base 3, because

1 times m-reduction [i] would yield (151, 241, 3121)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 701577 857929 714301 524143 043612 579410 284257 020627 676776 553416 417049 588254 219835 347932 478010 116999 460148 855116 813491 > 3²⁴¹ [i]