Best Known (65, ∞, s)-Nets in Base 5
(65, ∞, 82)-Net over F5 — Constructive and digital
Digital (65, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 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
(65, ∞, 120)-Net over F5 — Digital
Digital (65, m, 120)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 119)-sequence over F5, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 61 and N(F) ≥ 120, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
(65, ∞, 277)-Net in Base 5 — Upper bound on s
There is no (65, m, 278)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (65, 1107, 278)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51107, 278, S5, 4, 1042), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 698 829255 645529 543019 983781 658682 235776 851489 414000 637802 629038 037639 974305 992519 385576 365957 255161 764860 183588 423006 053869 482016 985382 480342 536439 598887 206431 775547 710978 841061 392645 187369 213970 356845 696001 841521 156609 242037 756044 396031 683525 833275 270300 314756 038754 937772 941849 403848 398095 925094 264529 672622 742440 758050 992518 552792 797951 522639 637931 072350 927113 552635 353346 549826 712238 281545 342854 148080 634061 524054 986209 274541 369856 200983 711173 228823 550759 768395 166454 792066 396086 105541 885172 976788 081219 093062 542842 234987 631671 850786 886849 677679 659073 188422 864390 491294 640482 287564 959537 783280 641437 372751 932924 837767 794926 993639 492742 747884 593348 353310 710673 968834 607253 934110 523959 913981 229074 379578 228407 381888 635149 167297 093658 439421 925976 375860 045664 012432 098388 671875 / 1043 > 51107 [i]
- extracting embedded OOA [i] would yield OOA(51107, 278, S5, 4, 1042), but