Best Known (143, ∞, s)-Nets in Base 5
(143, ∞, 124)-Net over F5 — Constructive and digital
Digital (143, m, 124)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 123)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 123)-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
- base reduction for sequences [i] based on digital (10, 123)-sequence over F25, using
(143, ∞, 230)-Net over F5 — Digital
Digital (143, m, 230)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 229)-sequence over F5, using
- t-expansion [i] based on digital (139, 229)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 139 and N(F) ≥ 230, using
- t-expansion [i] based on digital (139, 229)-sequence over F5, using
(143, ∞, 591)-Net in Base 5 — Upper bound on s
There is no (143, m, 592)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (143, 2363, 592)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52363, 592, S5, 4, 2220), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 110562 698351 968260 114238 274752 120530 249206 647867 029020 854086 110876 431423 346393 876381 425253 634256 968884 508197 419670 525104 644531 866679 117356 788855 747010 988337 150200 693270 513722 571100 767962 703266 825153 276924 574123 152189 123361 206520 653572 690593 499414 811081 226544 961038 893866 603494 460993 359950 419659 642847 885086 995481 467486 999050 483232 429159 103198 199606 331283 305382 170834 455910 337155 866889 921257 241076 741397 303047 359656 571745 487403 538889 636022 960978 401749 829664 415596 548088 818751 257660 986976 717694 899409 554545 612163 586112 280060 370617 015656 363181 307923 733071 399086 341257 566073 480371 422190 803266 440655 254270 494622 961057 437782 388781 461481 867907 325643 624489 236909 612237 195018 228620 776089 431275 041068 022575 063881 709268 696872 998709 301741 731914 771852 540245 242986 153832 256441 558477 444463 136135 312057 053714 529376 438474 463772 420936 489018 228262 770876 873893 415262 081641 673367 122913 578838 378770 961290 195785 938124 452057 474859 743509 935218 268556 735999 871750 131329 662926 828136 232442 441050 528485 701469 911290 846025 819434 630765 789111 885200 186009 669641 235756 009705 896811 331642 705885 085637 246178 328137 417451 214263 986881 196170 564428 214656 462772 753429 242890 393532 047512 874202 149706 692465 264262 849505 720447 759300 061647 884396 828242 301323 977223 588494 179709 415222 809841 072624 478550 578538 676208 903463 410609 943653 503663 866611 325523 849832 894351 299929 850941 328142 762524 819522 282296 682227 878389 543428 457162 061628 991755 380982 202345 383517 361356 936189 453927 866614 223964 192535 193811 438654 654622 425236 748502 107150 724038 749255 660193 193810 715013 249410 713890 314406 114137 690668 631112 463409 984743 933115 425847 121812 537999 146596 053204 133947 024787 876407 586573 204136 666526 142818 156586 145050 823688 507080 078125 / 2221 > 52363 [i]
- extracting embedded OOA [i] would yield OOA(52363, 592, S5, 4, 2220), but