MinT - Best Known (242−48, 242, s)-Nets in Base 3

Best Known (242−48, 242, s)-Nets in Base 3

(242−48, 242, 688)-Net over F₃ — Constructive and digital

Digital (194, 242, 688)-net over F₃, using

t-expansion [i] based on digital (193, 242, 688)-net over F₃, using
- 6 times m-reduction [i] based on digital (193, 248, 688)-net over F₃, using
  - trace code for nets [i] based on digital (7, 62, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(242−48, 242, 2652)-Net over F₃ — Digital

Digital (194, 242, 2652)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−48, 242, 317156)-Net in Base 3 — Upper bound on s

There is no (194, 242, 317157)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 064958 506716 713130 731539 408351 807671 738408 887642 965924 014415 256264 505690 371027 025688 389984 020745 252883 998481 229089 > 3²⁴² [i]