MinT - Best Known (67−43, 67, s)-Nets in Base 3

Best Known (67−43, 67, s)-Nets in Base 3

(67−43, 67, 32)-Net over F₃ — Constructive and digital

Digital (24, 67, 32)-net over F₃, using

t-expansion [i] based on digital (21, 67, 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]

(67−43, 67, 90)-Net in Base 3 — Upper bound on s

There is no (24, 67, 91)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁷, 91, S₃, 43), but
- the linear programming bound shows that MÂ â‰¥ 14877 993637 977476 431918 834321 910343 999390 452202 / 142 782236 368585 > 3⁶⁷ [i]