MinT - Best Known (94−58, 94, s)-Nets in Base 3

Best Known (94−58, 94, s)-Nets in Base 3

(94−58, 94, 38)-Net over F₃ — Constructive and digital

Digital (36, 94, 38)-net over F₃, using

t-expansion [i] based on digital (32, 94, 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]

(94−58, 94, 48)-Net over F₃ — Digital

Digital (36, 94, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(94−58, 94, 138)-Net in Base 3 — Upper bound on s

There is no (36, 94, 139)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁴, 139, S₃, 58), but
- the linear programming bound shows that MÂ â‰¥ 53 974723 561495 249210 853154 368191 961797 942003 645838 737596 383041 688100 468868 966257 / 73405 813563 072169 321364 692815 942025 > 3⁹⁴ [i]