MinT - Best Known (38, 38+62, s)-Nets in Base 3

Best Known (38, 38+62, s)-Nets in Base 3

(38, 38+62, 38)-Net over F₃ — Constructive and digital

Digital (38, 100, 38)-net over F₃, using

t-expansion [i] based on digital (32, 100, 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+62, 52)-Net over F₃ — Digital

Digital (38, 100, 52)-net over F₃, using

t-expansion [i] based on digital (37, 100, 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+62, 139)-Net in Base 3 — Upper bound on s

There is no (38, 100, 140)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁰, 140, S₃, 62), but
- the linear programming bound shows that MÂ â‰¥ 8 547581 834483 397749 537798 679986 213858 108532 179344 941208 590051 924529 547931 / 16 230715 477831 782311 672827 > 3¹⁰⁰ [i]