Best Known (12, s)-Sequences in Base 7
(12, 19)-Sequence over F7 — Constructive and digital
Digital (12, 19)-sequence over F7, using
(12, 37)-Sequence over F7 — Digital
Digital (12, 37)-sequence over F7, using
- t-expansion [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
(12, 87)-Sequence in Base 7 — Upper bound on s
There is no (12, 88)-sequence in base 7, because
- net from sequence [i] would yield (12, m, 89)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (12, 175, 89)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7175, 89, S7, 2, 163), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 709901 992001 094238 731882 235639 917450 777724 124562 630869 886177 412570 015953 611806 427131 972320 188924 690291 451754 641068 634534 618479 201039 535806 045365 852813 / 82 > 7175 [i]
- extracting embedded OOA [i] would yield OOA(7175, 89, S7, 2, 163), but
- m-reduction [i] would yield (12, 175, 89)-net in base 7, but