Best Known (157−130, 157, s)-Nets in Base 3
(157−130, 157, 37)-Net over F3 — Constructive and digital
Digital (27, 157, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
(157−130, 157, 39)-Net over F3 — Digital
Digital (27, 157, 39)-net over F3, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 27 and N(F) ≥ 39, using
(157−130, 157, 70)-Net in Base 3 — Upper bound on s
There is no (27, 157, 71)-net in base 3, because
- 20 times m-reduction [i] would yield (27, 137, 71)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3137, 71, S3, 2, 110), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 442979 136963 283965 427040 323903 217220 344490 744684 442124 765996 751335 / 37 > 3137 [i]
- extracting embedded OOA [i] would yield OOA(3137, 71, S3, 2, 110), but