MinT - Best Known (43, 43+20, s)-Nets in Base 3

Best Known (43, 43+20, s)-Nets in Base 3

(43, 43+20, 114)-Net over F₃ — Constructive and digital

Digital (43, 63, 114)-net over F₃, using

trace code for nets [i] based on digital (1, 21, 38)-net over F₂₇, using
- net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(43, 43+20, 153)-Net over F₃ — Digital

Digital (43, 63, 153)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+20, 2285)-Net in Base 3 — Upper bound on s

There is no (43, 63, 2286)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 146248 400062 332088 932117 369517 > 3⁶³ [i]