Best Known (30, 30+41, s)-Nets in Base 3
(30, 30+41, 37)-Net over F3 — Constructive and digital
Digital (30, 71, 37)-net over F3, using
- t-expansion [i] based on digital (27, 71, 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+41, 42)-Net over F3 — Digital
Digital (30, 71, 42)-net over F3, using
- t-expansion [i] based on digital (29, 71, 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+41, 172)-Net in Base 3 — Upper bound on s
There is no (30, 71, 173)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(371, 173, S3, 41), but
- the linear programming bound shows that M ≥ 752 213045 412644 622322 639569 681201 793647 412281 389251 969822 802871 486494 784732 933848 371039 162021 095359 451090 737034 712280 246898 192888 217335 028567 448906 630420 259126 393691 599101 660621 344716 988276 971065 655155 449564 286879 801625 / 99411 491410 035009 716994 001272 318459 880023 404946 768393 677017 035421 193893 190900 114748 467022 440016 060914 627280 959263 096693 535393 660281 132091 783126 909751 606063 233958 271183 758623 954372 067907 > 371 [i]