Best Known (144, s)-Sequences in Base 3
(144, 80)-Sequence over F3 — Constructive and digital
Digital (144, 80)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
(144, 119)-Sequence over F3 — Digital
Digital (144, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(144, 300)-Sequence in Base 3 — Upper bound on s
There is no (144, 301)-sequence in base 3, because
- net from sequence [i] would yield (144, m, 302)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (144, 1805, 302)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31805, 302, S3, 6, 1661), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 462128 349919 433055 991749 906320 519906 788853 573411 017242 800971 511225 093327 731670 338893 081435 148086 322353 276873 616004 843236 654707 163567 116118 314613 524559 002171 878594 927595 461487 690912 490879 554080 209850 374251 358623 871048 992822 320818 000867 068942 126702 879758 751276 968175 610255 781417 547932 458862 960210 888472 032021 815447 457393 630332 813568 741117 760815 551771 899022 726749 936340 073479 092287 302479 456741 839981 891728 896848 520251 000076 755942 353166 015130 589689 478239 308322 674630 097968 133200 052174 919466 720088 326934 194074 290601 635987 042173 385796 055322 447709 505771 783004 512621 561156 852379 721113 524361 572687 735695 717934 711697 525743 383802 314813 495662 382037 419647 449692 946134 502723 241438 283871 628514 552834 950352 267600 696387 961177 465876 516356 392830 104253 625104 873252 634708 572898 495364 779082 301555 084719 423042 314461 771698 599889 647927 120423 159076 193836 690622 398704 544126 071151 454858 962227 / 277 > 31805 [i]
- extracting embedded OOA [i] would yield OOA(31805, 302, S3, 6, 1661), but
- m-reduction [i] would yield (144, 1805, 302)-net in base 3, but