MinT - Best Known (108, 108+82, s)-Nets in Base 3

Best Known (108, 108+82, s)-Nets in Base 3

(108, 108+82, 128)-Net over F₃ — Constructive and digital

Digital (108, 190, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 95, 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]

(108, 108+82, 145)-Net over F₃ — Digital

Digital (108, 190, 145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+82, 1272)-Net in Base 3 — Upper bound on s

There is no (108, 190, 1273)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 639619 071398 929362 827197 153475 967787 206232 686402 029652 257217 253269 711558 696740 402209 746131 > 3¹⁹⁰ [i]