Best Known (85, 85+∞, s)-Nets in Base 5
(85, 85+∞, 82)-Net over F5 — Constructive and digital
Digital (85, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (85, 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
(85, 85+∞, 150)-Net over F5 — Digital
Digital (85, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (85, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(85, 85+∞, 358)-Net in Base 5 — Upper bound on s
There is no (85, m, 359)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (85, 1431, 359)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51431, 359, S5, 4, 1346), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 31 892269 043326 921716 699961 392987 644854 502034 050341 989249 646526 187661 242391 748697 437320 734027 326471 456873 275099 750263 415371 149727 677330 099506 100322 584737 156849 057904 144007 015091 946268 173774 870086 103126 967694 082776 734127 997127 255569 241457 353386 068495 267821 565007 476608 980921 216257 882795 286422 755113 420016 476404 705854 474200 669578 521065 429729 135552 470827 837934 436779 895704 439549 394033 358520 965303 670165 550111 147924 487333 424497 327795 010405 729751 229189 637586 576322 350318 244514 419987 193044 827434 858280 132126 325610 976346 626865 488246 681128 695279 336783 840325 085094 345539 970522 991882 701682 228403 693192 625102 614755 592480 237539 544495 229052 291612 417249 845363 518707 987389 835408 295653 631049 194428 768782 564174 053334 082635 880366 618121 048952 226454 427464 421681 138433 427590 123382 112936 383434 395267 395589 486820 885580 493330 133416 824907 510453 276590 985726 801145 744360 231834 663375 201701 888289 749966 976909 094168 237802 227059 470607 970249 929910 207837 101522 348577 221838 293158 422308 661322 557769 672580 985087 506633 135490 119457 244873 046875 / 1347 > 51431 [i]
- extracting embedded OOA [i] would yield OOA(51431, 359, S5, 4, 1346), but