MinT - Best Known (89, 122, s)-Nets in Base 3

Best Known (89, 122, s)-Nets in Base 3

(89, 122, 246)-Net over F₃ — Constructive and digital

Digital (89, 122, 246)-net over F₃, using

1 times m-reduction [i] based on digital (89, 123, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 41, 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]

(89, 122, 427)-Net over F₃ — Digital

Digital (89, 122, 427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 122, 13780)-Net in Base 3 — Upper bound on s

There is no (89, 122, 13781)-net in base 3, because

1 times m-reduction [i] would yield (89, 121, 13781)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5397 087636 747042 586160 544950 841118 188333 015076 977109 249473 > 3¹²¹ [i]