Best Known (16, s)-Sequences in Base 7
(16, 23)-Sequence over F7 — Constructive and digital
Digital (16, 23)-sequence over F7, using
(16, 47)-Sequence over F7 — Digital
Digital (16, 47)-sequence over F7, using
- t-expansion [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(16, 113)-Sequence in Base 7 — Upper bound on s
There is no (16, 114)-sequence in base 7, because
- net from sequence [i] would yield (16, m, 115)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (16, 227, 115)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7227, 115, S7, 2, 211), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 91 433790 468743 797104 637620 187509 466614 130620 064842 733617 237721 699459 080769 803041 509413 783468 175430 368539 431190 102825 053208 578400 210831 727682 045616 771417 670995 234693 480307 331075 252532 593228 839219 / 106 > 7227 [i]
- extracting embedded OOA [i] would yield OOA(7227, 115, S7, 2, 211), but
- m-reduction [i] would yield (16, 227, 115)-net in base 7, but