Best Known (131, s)-Sequences in Base 5
(131, 111)-Sequence over F5 — Constructive and digital
Digital (131, 111)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 111)-sequence over F25, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- s-reduction based on digital (10, 125)-sequence over F25, using
(131, 209)-Sequence over F5 — Digital
Digital (131, 209)-sequence over F5, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 127 and N(F) ≥ 210, using
(131, 542)-Sequence in Base 5 — Upper bound on s
There is no (131, 543)-sequence in base 5, because
- net from sequence [i] would yield (131, m, 544)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (131, 2171, 544)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52171, 544, S5, 4, 2040), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 711 472759 925474 051605 004616 684097 219095 226988 977199 902031 682206 859402 460315 856044 769386 397569 093433 978220 775094 822772 814728 191687 490192 455315 991529 296655 167778 799373 696133 493092 531840 325434 116510 580434 207350 980461 653169 637917 827465 929546 281543 313409 742323 113643 575551 968581 198568 181531 509880 079603 711157 959089 931206 680023 103742 748830 490648 253998 681647 358040 931277 582192 389555 212081 400175 530028 532641 502904 675940 442120 600619 374218 843368 587840 055119 385700 653822 494075 332995 984368 152015 048921 873204 483988 231391 451837 888250 394698 252917 730814 733018 401364 415053 205847 019656 598768 451396 005984 971526 542426 630829 518786 053177 219238 399558 588787 609305 234358 587899 913538 981519 711106 987164 543591 220720 908157 594244 826139 663406 949799 409392 752071 182808 658307 071968 577706 728950 071000 769369 902303 918255 589956 741945 812133 694048 274506 696836 045091 951429 447121 238303 228873 126436 167676 896290 893708 080354 251960 639924 760632 662907 793776 355535 419883 006271 701165 077406 250443 376039 490287 915354 641226 637203 840822 179822 056785 573828 010316 344818 957917 517675 082778 996977 333842 261088 090289 679254 921845 044622 379278 997737 582301 183005 840402 903514 142199 519784 391138 373098 872641 169641 466133 071172 088454 074191 224770 777161 312640 108282 786639 558385 230320 870531 864416 050829 951780 115017 972678 258632 465262 252185 925986 438071 573269 655256 191973 728812 584069 587569 548663 476741 069082 644489 791254 733177 675477 393778 658273 366891 418050 308930 410029 471440 341095 902768 625227 694275 366139 180017 287531 008030 154824 358816 088418 809487 524746 833588 852601 426566 479858 593083 918094 635009 765625 / 2041 > 52171 [i]
- extracting embedded OOA [i] would yield OOA(52171, 544, S5, 4, 2040), but
- m-reduction [i] would yield (131, 2171, 544)-net in base 5, but