MinT - Best Known (38, 38+63, s)-Nets in Base 3

Best Known (38, 38+63, s)-Nets in Base 3

(38, 38+63, 38)-Net over F₃ — Constructive and digital

Digital (38, 101, 38)-net over F₃, using

t-expansion [i] based on digital (32, 101, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(38, 38+63, 52)-Net over F₃ — Digital

Digital (38, 101, 52)-net over F₃, using

t-expansion [i] based on digital (37, 101, 52)-net over F₃, using
- net from sequence [i] based on digital (37, 51)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
    - a curve from the manYPoints database [i]

(38, 38+63, 136)-Net in Base 3 — Upper bound on s

There is no (38, 101, 137)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰¹, 137, S₃, 63), but
- the linear programming bound shows that MÂ â‰¥ 4263 647138 131785 298570 566140 299637 211456 325385 326443 606024 799471 478799 / 2418 084085 632422 207000 > 3¹⁰¹ [i]