MinT - Best Known (218−96, 218, s)-Nets in Base 3

Best Known (218−96, 218, s)-Nets in Base 3

(218−96, 218, 128)-Net over F₃ — Constructive and digital

Digital (122, 218, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 109, 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]

(218−96, 218, 154)-Net over F₃ — Digital

Digital (122, 218, 154)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−96, 218, 1329)-Net in Base 3 — Upper bound on s

There is no (122, 218, 1330)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 105 141101 823180 900085 976302 319030 135756 926579 035781 946295 923719 833980 205641 915487 000358 213162 469063 557089 > 3²¹⁸ [i]