Best Known (75, ∞, s)-Nets in Base 5
(75, ∞, 82)-Net over F5 — Constructive and digital
Digital (75, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 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
(75, ∞, 132)-Net over F5 — Digital
Digital (75, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 131)-sequence over F5, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
(75, ∞, 318)-Net in Base 5 — Upper bound on s
There is no (75, m, 319)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (75, 1271, 319)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51271, 319, S5, 4, 1196), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4784 043464 995452 862763 584555 605210 008252 475459 718307 547403 743919 184186 385396 659904 800121 057888 593561 554394 650283 827769 469897 526813 016605 812865 182039 292556 338387 159064 202663 509563 903430 436918 417590 629158 608056 443548 066567 832246 222146 312099 898738 269497 715404 495268 656640 155329 469187 331889 063468 895036 366364 986120 512175 168733 142370 544664 927325 726275 656150 415092 802247 231223 057020 808034 028298 024117 028084 882704 551707 216043 545133 639166 437525 616155 868113 352923 927874 266534 338283 614128 613935 361331 017378 889804 107654 956740 690076 926936 889891 823865 574411 768921 236864 381051 948009 803661 632789 367280 244230 343975 639730 841836 514753 332757 313761 606844 176495 033012 008097 496951 700256 099034 643959 718066 559418 859591 797131 220633 945640 841476 211986 685738 766201 157165 338156 205182 690798 745657 845652 307185 535955 109816 243961 991596 445790 929911 563491 136793 590863 097013 831172 369465 079274 863938 962880 638428 032398 223876 953125 / 1197 > 51271 [i]
- extracting embedded OOA [i] would yield OOA(51271, 319, S5, 4, 1196), but