MinT - Best Known (191, 191+53, s)-Nets in Base 3

Best Known (191, 191+53, s)-Nets in Base 3

(191, 191+53, 688)-Net over F₃ — Constructive and digital

Digital (191, 244, 688)-net over F₃, using

t-expansion [i] based on digital (190, 244, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 61, 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]

(191, 191+53, 1778)-Net over F₃ — Digital

Digital (191, 244, 1778)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191, 191+53, 151858)-Net in Base 3 — Upper bound on s

There is no (191, 244, 151859)-net in base 3, because

1 times m-reduction [i] would yield (191, 243, 151859)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 198814 220332 150722 728725 460600 915354 300756 489051 898432 906329 797803 892394 562779 662740 199289 909535 108472 688763 007509 > 3²⁴³ [i]