Best Known (92, ∞, s)-Nets in Base 5
(92, ∞, 82)-Net over F5 — Constructive and digital
Digital (92, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 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
(92, ∞, 150)-Net over F5 — Digital
Digital (92, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 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
(92, ∞, 386)-Net in Base 5 — Upper bound on s
There is no (92, m, 387)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (92, 1543, 387)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51543, 387, S5, 4, 1451), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 023985 631385 010131 021144 476896 659108 375103 626733 440105 993708 525163 670650 587861 210478 026459 405338 817399 694839 041821 884827 727536 477684 881769 244640 382368 084465 519677 287297 552338 302121 606014 439541 537578 830435 093570 777510 819646 835654 986640 712197 124064 226103 024075 856325 785598 327671 079298 127026 604449 594117 301805 575413 045655 583704 569965 514008 110132 509757 442040 497845 935963 319519 062852 224634 938107 083137 865959 028083 238469 596081 077505 013395 254572 431878 103485 464031 296794 135441 003795 993602 017852 413259 972156 379653 344228 959476 212300 678606 488825 465392 190800 536603 127766 340518 272153 833568 877278 897247 273265 475045 666306 734174 403971 004543 638729 293540 822226 077513 867134 441253 453114 968614 084231 865995 622628 444522 760715 762828 500057 166035 770096 974527 166805 413369 950131 620670 030043 990702 056400 411525 751583 447763 946203 107867 170025 853037 276839 290702 183040 502769 342721 882919 490116 341046 826804 162216 513691 151618 785280 955635 341907 848264 169395 368656 062096 771325 858681 518491 368345 165481 544908 388741 876839 405150 894022 989206 919930 710783 222395 829149 773229 531605 495969 646957 288290 423093 712888 658046 722412 109375 / 121 > 51543 [i]
- extracting embedded OOA [i] would yield OOA(51543, 387, S5, 4, 1451), but