MinT - Best Known (191−83, 191, s)-Nets in Base 3

Best Known (191−83, 191, s)-Nets in Base 3

(191−83, 191, 80)-Net over F₃ — Constructive and digital

Digital (108, 191, 80)-net over F₃, using

9 times m-reduction [i] based on digital (108, 200, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 100, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(191−83, 191, 142)-Net over F₃ — Digital

Digital (108, 191, 142)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−83, 191, 1272)-Net in Base 3 — Upper bound on s

There is no (108, 191, 1273)-net in base 3, because

1 times m-reduction [i] would yield (108, 190, 1273)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 639619 071398 929362 827197 153475 967787 206232 686402 029652 257217 253269 711558 696740 402209 746131 > 3¹⁹⁰ [i]