Best Known (145, s)-Sequences in Base 3
(145, 80)-Sequence over F3 — Constructive and digital
Digital (145, 80)-sequence over F3, using
- t-expansion [i] based on 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
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
(145, 119)-Sequence over F3 — Digital
Digital (145, 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
(145, 302)-Sequence in Base 3 — Upper bound on s
There is no (145, 303)-sequence in base 3, because
- net from sequence [i] would yield (145, m, 304)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (145, 1817, 304)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31817, 304, S3, 6, 1672), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 471014 296266 098113 182762 331353 678891 507663 506336 444157 625737 009178 766155 466621 776074 653202 354258 138216 406462 802940 314697 000642 323991 949520 500112 203072 778980 460381 754782 164192 106529 119683 103889 264810 219852 234179 792388 684540 681637 576654 380107 956894 633100 200346 748774 170526 265984 952491 797820 041685 811781 955739 655480 208741 815513 218141 468643 660744 549864 298075 977232 318553 398399 127176 635587 200635 497767 212457 077978 888838 000026 749695 466257 807361 883055 198458 871613 188664 811525 963017 654720 345925 253054 281035 919869 147781 941857 961022 499658 742307 210765 908262 381833 822711 249855 555217 144631 537432 224675 903250 164596 827257 483431 621632 373851 726572 761329 186739 249828 849882 073699 223761 918428 814207 597512 242109 432529 392054 869059 351957 883296 975384 299534 188578 098048 320790 230768 013824 535684 568219 009108 536171 917085 223298 893097 110860 787920 816148 790852 220406 684175 740380 684251 568708 877925 210153 / 1673 > 31817 [i]
- extracting embedded OOA [i] would yield OOA(31817, 304, S3, 6, 1672), but
- m-reduction [i] would yield (145, 1817, 304)-net in base 3, but