MinT - Best Known (122, 122+43, s)-Nets in Base 3

Best Known (122, 122+43, s)-Nets in Base 3

(122, 122+43, 288)-Net over F₃ — Constructive and digital

Digital (122, 165, 288)-net over F₃, using

t-expansion [i] based on digital (121, 165, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 55, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(122, 122+43, 619)-Net over F₃ — Digital

Digital (122, 165, 619)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+43, 23076)-Net in Base 3 — Upper bound on s

There is no (122, 165, 23077)-net in base 3, because

1 times m-reduction [i] would yield (122, 164, 23077)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 770710 180858 428456 065034 297848 980439 873470 089960 918601 844930 643147 932030 739995 > 3¹⁶⁴ [i]