MinT - Best Known (122−54, 122, s)-Nets in Base 3

Best Known (122−54, 122, s)-Nets in Base 3

(122−54, 122, 72)-Net over F₃ — Constructive and digital

Digital (68, 122, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 61, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(122−54, 122, 93)-Net over F₃ — Digital

Digital (68, 122, 93)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−54, 122, 755)-Net in Base 3 — Upper bound on s

There is no (68, 122, 756)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16195 051632 540465 808254 361039 117617 336866 850517 375642 477617 > 3¹²² [i]