Best Known (29, 29+50, s)-Nets in Base 3
(29, 29+50, 37)-Net over F3 — Constructive and digital
Digital (29, 79, 37)-net over F3, using
- t-expansion [i] based on digital (27, 79, 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
(29, 29+50, 42)-Net over F3 — Digital
Digital (29, 79, 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
(29, 29+50, 107)-Net in Base 3 — Upper bound on s
There is no (29, 79, 108)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(379, 108, S3, 50), but
- the linear programming bound shows that M ≥ 17 534511 337853 558668 492502 167227 612507 359380 469822 536899 / 298348 310384 556250 > 379 [i]