MinT - Best Known (35, 93, s)-Nets in Base 3

Best Known (35, 93, s)-Nets in Base 3

(35, 93, 38)-Net over F₃ — Constructive and digital

Digital (35, 93, 38)-net over F₃, using

t-expansion [i] based on digital (32, 93, 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]

(35, 93, 47)-Net over F₃ — Digital

Digital (35, 93, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(35, 93, 128)-Net in Base 3 — Upper bound on s

There is no (35, 93, 129)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹³, 129, S₃, 58), but
- the linear programming bound shows that MÂ â‰¥ 1026 671326 255502 952333 970392 423627 646105 652721 499920 138275 737785 004893 / 4 227606 657819 243019 378057 > 3⁹³ [i]