Best Known (68−57, 68, s)-Nets in Base 3
(68−57, 68, 20)-Net over F3 — Constructive and digital
Digital (11, 68, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
(68−57, 68, 32)-Net in Base 3 — Upper bound on s
There is no (11, 68, 33)-net in base 3, because
- 6 times m-reduction [i] would yield (11, 62, 33)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(362, 33, S3, 2, 51), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 301051 460877 537453 973547 267843 / 26 > 362 [i]
- extracting embedded OOA [i] would yield OOA(362, 33, S3, 2, 51), but