MinT - Best Known (191−61, 191, s)-Nets in Base 3

Best Known (191−61, 191, s)-Nets in Base 3

(191−61, 191, 162)-Net over F₃ — Constructive and digital

Digital (130, 191, 162)-net over F₃, using

5 times m-reduction [i] based on digital (130, 196, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 98, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(191−61, 191, 351)-Net over F₃ — Digital

Digital (130, 191, 351)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−61, 191, 6302)-Net in Base 3 — Upper bound on s

There is no (130, 191, 6303)-net in base 3, because

1 times m-reduction [i] would yield (130, 190, 6303)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 512091 395632 286899 369867 771274 744649 051410 001563 421791 243260 148638 212169 718875 306521 056261 > 3¹⁹⁰ [i]