Best Known (131, ∞, s)-Nets in Base 4
(131, ∞, 130)-Net over F4 — Constructive and digital
Digital (131, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (131, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(131, ∞, 176)-Net over F4 — Digital
Digital (131, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (131, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(131, ∞, 409)-Net in Base 4 — Upper bound on s
There is no (131, m, 410)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (131, 2044, 410)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42044, 410, S4, 5, 1913), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1484 990440 759326 220452 335885 550200 293980 886666 614248 812733 831984 044371 962897 058258 956925 623220 074653 265953 120484 593326 847763 580982 420425 285327 413812 413660 004579 407576 023087 653890 201635 972326 849478 327412 048107 673540 628828 349768 622810 252850 879302 459096 753273 745191 064641 726357 006802 356147 334634 155911 053447 493882 991357 753792 008143 256442 926777 274915 027035 349795 870415 241084 004974 551194 585756 061906 150223 345922 436711 898832 108744 534586 550043 781107 506409 284050 533081 293168 121343 009569 273809 662193 752250 007188 008267 501070 454525 257592 256007 117361 737251 818075 980693 142812 232015 929678 516727 591333 398802 740976 503224 668589 221080 724875 595396 102892 837453 431062 068509 552467 477937 352131 414037 197010 915741 293580 348013 576783 792124 517755 552271 196116 895732 163030 261240 072675 207479 230025 518785 049513 007335 328617 052035 138178 775641 452114 335696 670881 951250 987393 588578 243566 281004 814000 885540 282131 526623 400031 554005 017004 456963 084768 393208 882192 663424 999001 663605 607772 547845 521632 438490 162098 750444 545022 431941 605495 271273 294662 693420 905288 515496 347311 647078 966694 032267 554511 065438 094201 874531 508235 415255 451384 175345 692533 420149 179735 033366 962690 806114 828403 858843 396632 403393 329976 869148 660392 613479 698867 390247 902986 533766 291940 815409 819671 510734 864384 / 319 > 42044 [i]
- extracting embedded OOA [i] would yield OOA(42044, 410, S4, 5, 1913), but