MinT - Best Known (102−63, 102, s)-Nets in Base 3

Best Known (102−63, 102, s)-Nets in Base 3

(102−63, 102, 42)-Net over F₃ — Constructive and digital

Digital (39, 102, 42)-net over F₃, using

net from sequence [i] based on digital (39, 41)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(102−63, 102, 52)-Net over F₃ — Digital

Digital (39, 102, 52)-net over F₃, using

t-expansion [i] based on digital (37, 102, 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]

(102−63, 102, 144)-Net in Base 3 — Upper bound on s

There is no (39, 102, 145)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰², 145, S₃, 63), but
- the linear programming bound shows that MÂ â‰¥ 776506 070804 940797 482287 435756 684689 957091 430666 641508 706084 490920 965603 695219 / 159956 166343 221247 242988 544800 > 3¹⁰² [i]