Best Known (110, s)-Sequences in Base 3
(110, 73)-Sequence over F3 — Constructive and digital
Digital (110, 73)-sequence over F3, using
- t-expansion [i] based on digital (107, 73)-sequence over F3, using
- base reduction for sequences [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
- base reduction for sequences [i] based on digital (17, 73)-sequence over F9, using
(110, 103)-Sequence over F3 — Digital
Digital (110, 103)-sequence over F3, using
- t-expansion [i] based on digital (102, 103)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 102 and N(F) ≥ 104, using
(110, 232)-Sequence in Base 3 — Upper bound on s
There is no (110, 233)-sequence in base 3, because
- net from sequence [i] would yield (110, m, 234)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (110, 1163, 234)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31163, 234, S3, 5, 1053), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 442183 260668 078198 608580 364062 877624 278758 640487 864399 430378 663085 738357 931634 449565 058126 223011 395300 339206 859616 430202 153050 470978 849416 269535 235285 127642 992075 405893 537104 670960 711174 946505 026753 465157 437798 033853 464443 519459 698062 681854 610725 311358 481182 950996 221595 289674 349155 096090 663117 963009 859930 222540 094675 105670 608299 535687 855213 852302 926688 002885 991764 100113 992412 222696 894558 423256 418311 186120 994716 429257 022914 552879 907120 159610 828628 429525 431184 554808 213771 486879 074038 449118 269813 662701 107866 491078 203054 394824 663770 721801 626183 972484 752109 / 527 > 31163 [i]
- extracting embedded OOA [i] would yield OOA(31163, 234, S3, 5, 1053), but
- m-reduction [i] would yield (110, 1163, 234)-net in base 3, but