Best Known (94, ∞, s)-Nets in Base 5
(94, ∞, 82)-Net over F5 — Constructive and digital
Digital (94, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 155)-Net over F5 — Digital
Digital (94, m, 155)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 154)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 94 and N(F) ≥ 155, using
(94, ∞, 394)-Net in Base 5 — Upper bound on s
There is no (94, m, 395)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (94, 1575, 395)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51575, 395, S5, 4, 1481), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 698069 337189 307852 617338 576313 440128 446912 761706 803609 593648 281095 068083 384130 092952 426654 399333 342383 272844 654190 270450 333910 129282 160216 965155 669050 963855 469554 526123 043376 971856 733838 660548 759903 821576 335850 888141 807675 440191 991663 666920 066444 535100 606851 485092 395928 365853 727517 404308 063295 921394 677197 343948 787984 260226 739152 620104 517347 956185 264255 650297 571989 988631 048080 287240 943983 956075 262340 221460 457348 110991 709879 469936 204425 194373 901952 066222 768988 126120 218903 681636 137003 602139 392543 922265 472342 979330 493854 978829 472380 353120 993295 638845 736759 303945 717813 731929 949977 912843 006238 005517 177003 425142 115473 684044 084034 709398 854127 202077 908005 709333 201709 796159 021663 701228 729979 662522 606560 972521 676795 028177 583791 390878 182820 105649 891981 156410 676125 360622 671909 026540 413290 786343 844523 033724 606919 480015 956507 746956 329088 607782 203887 039750 533292 252610 695156 877146 954973 305672 794157 591672 838224 632792 348566 482505 559416 474816 001723 431021 413092 783572 697387 145950 284107 024896 255569 842706 584782 596117 919118 074814 930233 340820 820907 780275 032956 009154 130557 793627 165352 745578 275062 143802 642822 265625 / 741 > 51575 [i]
- extracting embedded OOA [i] would yield OOA(51575, 395, S5, 4, 1481), but