MinT - Best Known (169, 169+73, s)-Nets in Base 3

Best Known (169, 169+73, s)-Nets in Base 3

(169, 169+73, 246)-Net over F₃ — Constructive and digital

Digital (169, 242, 246)-net over F₃, using

1 times m-reduction [i] based on digital (169, 243, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 81, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(169, 169+73, 515)-Net over F₃ — Digital

Digital (169, 242, 515)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+73, 11127)-Net in Base 3 — Upper bound on s

There is no (169, 242, 11128)-net in base 3, because

1 times m-reduction [i] would yield (169, 241, 11128)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 711634 506445 823727 436466 744876 267146 479079 757528 534683 799667 380909 219994 545647 419683 417216 345087 384590 593809 467329 > 3²⁴¹ [i]