MinT - Best Known (21, 21+42, s)-Nets in Base 3

Best Known (21, 21+42, s)-Nets in Base 3

(21, 21+42, 32)-Net over F₃ — Constructive and digital

Digital (21, 63, 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]

(21, 21+42, 73)-Net in Base 3 — Upper bound on s

There is no (21, 63, 74)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶³, 74, S₃, 42), but
- the linear programming bound shows that MÂ â‰¥ 12 034337 282839 174538 591498 251772 066709 / 10 069525 > 3⁶³ [i]