Best Known (32, s)-Sequences in Base 8
(32, 64)-Sequence over F8 — Constructive and digital
Digital (32, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
(32, 96)-Sequence over F8 — Digital
Digital (32, 96)-sequence over F8, using
- t-expansion [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
(32, 245)-Sequence in Base 8 — Upper bound on s
There is no (32, 246)-sequence in base 8, because
- net from sequence [i] would yield (32, m, 247)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (32, 737, 247)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8737, 247, S8, 3, 705), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 167 765781 082904 582240 689917 054821 757676 174686 343149 409322 396267 549820 214338 013965 702033 627558 381784 188400 726360 060015 956969 697686 632846 100778 399163 956899 757051 046597 963356 925354 153949 627175 951477 540136 742713 586142 477484 474462 959913 773511 478895 982102 151719 693510 976771 497711 457900 397067 671857 775593 168343 312419 779176 898671 062527 383606 013626 211189 749393 916783 814974 526807 422695 060358 013182 997615 879462 702445 109108 944944 642298 631970 107524 139446 401331 693141 020366 186533 024065 878914 202899 293588 342098 863205 296858 407018 893973 887057 318487 799647 280894 666403 058910 473383 779735 553603 988981 114722 148969 226287 773891 248480 014345 941774 909906 435065 551764 572793 647681 785060 815443 853312 / 353 > 8737 [i]
- extracting embedded OOA [i] would yield OOA(8737, 247, S8, 3, 705), but
- m-reduction [i] would yield (32, 737, 247)-net in base 8, but