Best Known (30, 30+54, s)-Nets in Base 3
(30, 30+54, 37)-Net over F3 — Constructive and digital
Digital (30, 84, 37)-net over F3, using
- t-expansion [i] based on digital (27, 84, 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
(30, 30+54, 42)-Net over F3 — Digital
Digital (30, 84, 42)-net over F3, using
- t-expansion [i] based on digital (29, 84, 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
(30, 30+54, 105)-Net in Base 3 — Upper bound on s
There is no (30, 84, 106)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(384, 106, S3, 54), but
- the linear programming bound shows that M ≥ 554636 234644 780595 906506 938993 021399 906097 624808 134107 / 34 652730 233275 > 384 [i]