MinT - Best Known (122−48, 122, s)-Nets in Base 3

Best Known (122−48, 122, s)-Nets in Base 3

(122−48, 122, 128)-Net over F₃ — Constructive and digital

Digital (74, 122, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 61, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(122−48, 122, 129)-Net over F₃ — Digital

Digital (74, 122, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−48, 122, 1281)-Net in Base 3 — Upper bound on s

There is no (74, 122, 1282)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16190 508876 890479 200134 952212 596521 594422 192255 021938 677489 > 3¹²² [i]