Best Known (19, s)-Sequences in Base 9
(19, 73)-Sequence over F9 — Constructive and digital
Digital (19, 73)-sequence over F9, using
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
(19, 83)-Sequence over F9 — Digital
Digital (19, 83)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 19 and N(F) ≥ 84, using
(19, 172)-Sequence in Base 9 — Upper bound on s
There is no (19, 173)-sequence in base 9, because
- net from sequence [i] would yield (19, m, 174)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (19, 345, 174)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9345, 174, S9, 2, 326), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19 136020 092621 986674 220659 413168 430069 475008 425255 137981 694464 368152 546340 183673 886309 531349 165896 101380 895402 249119 551765 847255 762024 027942 836069 129196 522961 741369 664871 345719 553644 091713 590504 032652 614654 081645 262386 095429 668357 613551 982143 255911 602653 476901 337135 687997 951859 010022 240454 339427 013160 244605 035669 240704 033288 205533 / 109 > 9345 [i]
- extracting embedded OOA [i] would yield OOA(9345, 174, S9, 2, 326), but
- m-reduction [i] would yield (19, 345, 174)-net in base 9, but