MinT - Best Known (65−42, 65, s)-Nets in Base 3

Best Known (65−42, 65, s)-Nets in Base 3

(65−42, 65, 32)-Net over F₃ — Constructive and digital

Digital (23, 65, 32)-net over F₃, using

t-expansion [i] based on digital (21, 65, 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]

(65−42, 65, 85)-Net in Base 3 — Upper bound on s

There is no (23, 65, 86)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁵, 86, S₃, 42), but
- the linear programming bound shows that MÂ â‰¥ 105639 517822 541973 415942 878050 095499 770611 / 8844 615395 > 3⁶⁵ [i]