Best Known (47, ∞, s)-Nets in Base 16
(47, ∞, 225)-Net over F16 — Constructive and digital
Digital (47, m, 225)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (47, 224)-sequence over F16, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
(47, ∞, 243)-Net over F16 — Digital
Digital (47, m, 243)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (47, 242)-sequence over F16, using
- t-expansion [i] based on digital (46, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 46 and N(F) ≥ 243, using
- t-expansion [i] based on digital (46, 242)-sequence over F16, using
(47, ∞, 743)-Net in Base 16 — Upper bound on s
There is no (47, m, 744)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (47, 1485, 744)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161485, 744, S16, 2, 1438), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2184 376853 837109 105102 502013 027409 624224 580779 304428 503326 047918 565673 388137 808758 087765 673682 765435 538634 010143 296721 043948 691231 916347 749242 014551 367556 785734 239132 547393 844357 054463 550061 930472 116808 452234 180705 914673 829971 826999 389252 144082 738080 917765 974694 774644 354609 612971 330263 443536 398375 986542 645977 101272 506462 513602 646147 426530 946234 278414 604390 255991 448008 382261 132390 518353 272980 652137 485315 191034 707971 589460 877269 540091 879714 083996 191354 761285 935863 871092 505337 871356 760716 814938 016882 418191 083214 367658 741927 009703 283277 874974 904124 889930 662231 250388 742464 267116 274643 721166 103551 344003 319176 329735 826217 076108 846109 511904 113128 620270 921423 785798 178128 131225 378176 830019 865377 373670 740968 820652 922440 712902 678804 685209 527377 588603 055015 494200 713135 011273 978973 092728 325437 564131 857549 237468 852503 098155 643528 879826 399348 793449 284592 344592 877953 949049 973895 071770 226918 450948 282838 199672 793420 078516 416353 155600 409399 182867 313448 596476 930634 974614 969027 392855 553576 488549 247849 495673 032381 854325 521711 221528 919353 444541 167670 726033 462646 809464 473264 331297 795518 609432 904093 230087 422724 934298 485589 033774 774935 251464 942303 333632 623588 860832 600545 123853 215564 031302 838409 322027 749915 125314 316148 396921 745887 949198 542151 370920 006785 767242 454968 139844 404544 149011 920674 207334 849162 536113 853187 833716 312535 078880 055248 729865 724396 464579 889318 791836 037965 916869 253026 198446 310370 517219 642136 331700 414261 699447 107768 249654 518794 917054 460764 256996 265879 418511 219402 390258 825259 299028 699387 366141 363643 402673 955250 692788 012569 311730 433008 085435 514442 014167 906741 553724 300074 484976 586961 750290 244873 089150 142731 866000 588118 870505 755208 740531 798423 263740 450769 642017 834016 804253 518567 117205 386660 281983 843026 767125 767346 341107 988742 812307 319694 456862 748170 158963 062638 908720 206539 915264 / 1439 > 161485 [i]
- extracting embedded OOA [i] would yield OOA(161485, 744, S16, 2, 1438), but