MinT - Best Known (38, 99, s)-Nets in Base 3

Best Known (38, 99, s)-Nets in Base 3

(38, 99, 38)-Net over F₃ — Constructive and digital

Digital (38, 99, 38)-net over F₃, using

t-expansion [i] based on digital (32, 99, 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, 99, 52)-Net over F₃ — Digital

Digital (38, 99, 52)-net over F₃, using

t-expansion [i] based on digital (37, 99, 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, 99, 143)-Net in Base 3 — Upper bound on s

There is no (38, 99, 144)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁹, 144, S₃, 61), but
- the linear programming bound shows that MÂ â‰¥ 60 189618 041602 458131 986507 057345 753786 899077 743068 445639 623337 673681 707308 116463 / 349 450505 963100 537827 386474 609375 > 3⁹⁹ [i]