Best Known (138, ∞, s)-Nets in Base 5
(138, ∞, 119)-Net over F5 — Constructive and digital
Digital (138, m, 119)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (138, 118)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 118)-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, 118)-sequence over F25, using
(138, ∞, 210)-Net over F5 — Digital
Digital (138, m, 210)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (138, 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
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
(138, ∞, 571)-Net in Base 5 — Upper bound on s
There is no (138, m, 572)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (138, 2283, 572)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52283, 572, S5, 4, 2145), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 675 315854 810774 332034 265223 040711 835093 976194 016387 509988 402291 392505 890585 365337 886149 119468 686086 255635 401978 275450 191235 747517 391287 197779 728898 511482 923494 896695 955008 684412 941248 205500 416780 812692 564764 536093 887228 518533 775997 126132 688399 173601 364785 979608 456789 805106 600460 168167 023360 489443 031747 572676 940700 796092 927320 674684 685344 111378 423033 054495 775563 308998 495018 011342 542919 861392 167276 186409 417346 091951 174627 651130 706196 993769 789731 675501 896959 370315 956399 507160 826792 307390 621279 149982 918278 669091 967447 558591 122460 907140 989290 341468 276121 869845 502310 366297 740431 497288 029490 648522 767766 602799 765168 958463 814258 496294 344349 893956 325494 728822 799912 003493 050786 460217 367154 886001 429187 470835 696401 783686 221833 155968 470441 428478 383433 538595 438446 382201 244013 502506 820242 852633 194003 819813 563533 328182 574683 073456 270293 203515 204233 195352 489231 221618 623881 661765 494635 732009 515075 881843 655725 427403 735769 888056 147915 128355 426291 709555 191225 926229 425066 975485 635855 654766 392415 124875 247041 765910 094315 035731 634677 882440 361486 525162 955547 192846 342847 583146 266883 468984 249908 746870 564489 724405 602274 028757 471578 776272 749528 639668 438972 996530 007797 233804 789677 641804 753115 177268 933988 793449 346351 436895 101842 688981 166891 565921 239612 675297 508254 307862 096891 576931 738113 734817 343638 176935 616102 326210 611670 951579 930210 286258 041069 876551 738230 554908 468219 644166 952140 865240 348817 671029 785648 611841 127914 338396 856241 635986 529068 558550 158425 700080 034020 946824 335430 717899 304693 366021 203434 067617 215309 301601 009485 768335 120284 355571 252618 876127 071643 710440 308761 011607 430191 361345 350742 340087 890625 / 1073 > 52283 [i]
- extracting embedded OOA [i] would yield OOA(52283, 572, S5, 4, 2145), but