Best Known (8, s)-Sequences in Base 7
(8, 15)-Sequence over F7 — Constructive and digital
Digital (8, 15)-sequence over F7, using
(8, 31)-Sequence over F7 — Digital
Digital (8, 31)-sequence over F7, using
- t-expansion [i] based on digital (7, 31)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 7 and N(F) ≥ 32, using
(8, 62)-Sequence in Base 7 — Upper bound on s
There is no (8, 63)-sequence in base 7, because
- net from sequence [i] would yield (8, m, 64)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (8, 125, 64)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7125, 64, S7, 2, 117), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 333999 431003 545482 755376 316309 265495 380733 140585 771192 834356 762366 331846 319516 550942 904758 800305 436017 702139 / 59 > 7125 [i]
- extracting embedded OOA [i] would yield OOA(7125, 64, S7, 2, 117), but
- m-reduction [i] would yield (8, 125, 64)-net in base 7, but