Best Known (59, ∞, s)-Nets in Base 5
(59, ∞, 82)-Net over F5 — Constructive and digital
Digital (59, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (59, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(59, ∞, 112)-Net over F5 — Digital
Digital (59, m, 112)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (59, 111)-sequence over F5, using
- t-expansion [i] based on digital (57, 111)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 57 and N(F) ≥ 112, using
- t-expansion [i] based on digital (57, 111)-sequence over F5, using
(59, ∞, 253)-Net in Base 5 — Upper bound on s
There is no (59, m, 254)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (59, 1011, 254)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51011, 254, S5, 4, 952), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 56 734043 214673 217985 481517 733454 705867 835881 383436 352082 716521 144823 183797 111360 590614 170275 237400 997934 363401 526058 694684 974705 277625 504471 567061 397406 923413 664124 967881 582621 636907 695432 020519 107427 296940 921183 213351 468794 967654 763303 073610 895595 910367 162191 101609 814147 456968 490375 694893 163590 014711 136617 722844 946220 499383 197207 945485 646944 871981 366976 439332 428487 282268 638870 911503 057933 230365 514847 642536 465176 192491 838672 386273 886109 874617 709439 977890 028911 608875 352797 039035 471141 802686 058546 776469 277556 492367 202077 019752 058921 777461 578175 640012 637899 376073 878791 566046 143687 197255 386716 949523 216410 297404 609727 783382 743113 780760 760960 417825 971292 647027 505195 479746 280540 211955 667473 375797 271728 515625 / 953 > 51011 [i]
- extracting embedded OOA [i] would yield OOA(51011, 254, S5, 4, 952), but