Best Known (4, s)-Sequences in Base 81
(4, 149)-Sequence over F81 — Constructive and digital
Digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
(4, 153)-Sequence over F81 — Digital
Digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
(4, 409)-Sequence in Base 81 — Upper bound on s
There is no (4, 410)-sequence in base 81, because
- net from sequence [i] would yield (4, m, 411)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (4, 409, 411)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81409, 411, S81, 405), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 903 605768 978992 104763 925948 119340 679791 249080 534251 635970 684159 912097 683773 884581 349485 563007 491443 884144 379866 373722 452477 977589 745175 755716 452198 434601 318505 021779 733918 497427 531688 765243 383931 843246 713940 449398 209704 748310 862411 696365 441532 112018 812574 475768 447795 642003 186603 730585 727981 117263 047636 040663 351311 594825 330720 376918 716312 251267 216415 826408 005188 312103 284618 115858 910886 743222 069994 994122 858356 811777 901432 014354 303989 519600 855360 675104 892830 005554 577172 204061 954733 845596 957724 420420 464710 576344 738206 470407 913866 468451 634153 393331 757603 798427 482958 987498 602458 614567 225253 170164 436555 706994 903041 066915 731958 587657 160630 883889 031312 702812 485702 140530 025313 954387 640975 669904 845455 781067 422188 292699 828483 152308 628774 130667 306935 010855 504773 529805 215475 329384 642403 / 203 > 81409 [i]
- extracting embedded OOA [i] would yield OA(81409, 411, S81, 405), but
- m-reduction [i] would yield (4, 409, 411)-net in base 81, but