MinT - Best Known (64−41, 64, s)-Nets in Base 3

Best Known (64−41, 64, s)-Nets in Base 3

(64−41, 64, 32)-Net over F₃ — Constructive and digital

Digital (23, 64, 32)-net over F₃, using

t-expansion [i] based on digital (21, 64, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(64−41, 64, 88)-Net in Base 3 — Upper bound on s

There is no (23, 64, 89)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁴, 89, S₃, 41), but
- the linear programming bound shows that MÂ â‰¥ 270 344305 793094 767616 866429 490879 306189 053619 / 74 160889 643750 > 3⁶⁴ [i]