Best Known (155−124, 155, s)-Nets in Base 3
(155−124, 155, 37)-Net over F3 — Constructive and digital
Digital (31, 155, 37)-net over F3, using
- t-expansion [i] based on digital (27, 155, 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]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(155−124, 155, 42)-Net over F3 — Digital
Digital (31, 155, 42)-net over F3, using
- t-expansion [i] based on digital (29, 155, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
(155−124, 155, 79)-Net in Base 3 — Upper bound on s
There is no (31, 155, 80)-net in base 3, because
- extracting embedded OOA [i] would yield OOA(3155, 80, S3, 2, 124), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2427 494450 315468 069358 961833 665581 682507 450011 656972 431201 424883 184770 261689 / 25 > 3155 [i]