MinT - Best Known (30, 57, s)-Nets in Base 3

Best Known (30, 57, s)-Nets in Base 3

(30, 57, 37)-Net over F₃ — Constructive and digital

Digital (30, 57, 37)-net over F₃, using

t-expansion [i] based on digital (27, 57, 37)-net over F₃, using
- net from sequence [i] based on digital (27, 36)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]

(30, 57, 44)-Net over F₃ — Digital

Digital (30, 57, 44)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 57, 309)-Net in Base 3 — Upper bound on s

There is no (30, 57, 310)-net in base 3, because

1 times m-reduction [i] would yield (30, 56, 310)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 532 729868 150153 808260 411061 > 3⁵⁶ [i]