Best Known (50, ∞, s)-Nets in Base 32
(50, ∞, 120)-Net over F32 — Constructive and digital
Digital (50, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
(50, ∞, 325)-Net over F32 — Digital
Digital (50, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 324)-sequence over F32, using
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 44 and N(F) ≥ 325, using
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
(50, ∞, 1616)-Net in Base 32 — Upper bound on s
There is no (50, m, 1617)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (50, 3231, 1617)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323231, 1617, S32, 2, 3181), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 493322 049838 756871 518515 547443 965086 268967 493699 731349 946616 280778 394127 719160 796778 833454 773149 090422 278743 451547 984524 298899 471875 127696 515018 753487 857768 367787 389989 614249 958660 963972 555071 078676 302265 280997 425186 022740 690464 314388 630769 956102 598813 576464 867649 640478 188025 899054 459131 265828 123539 757659 384096 841344 885040 961128 649764 179578 377563 590914 120294 083763 596872 166262 785190 669811 291021 119111 918773 311745 517539 693980 645310 102863 875681 253200 617484 446825 946043 863233 784756 663942 103910 908142 546084 159782 252556 521909 480585 909828 865150 241343 231169 048597 478113 862276 967383 738301 645970 245862 140237 839979 874522 179971 842977 459477 432718 663475 864806 099534 947985 880297 053559 519272 819081 482452 878407 764876 199823 309978 450486 510544 004550 008395 190994 435088 540169 973453 254285 784444 197906 904160 306286 419160 465985 589076 070229 662968 977787 649750 834217 685463 780862 541961 385396 874924 083982 962011 829837 906053 019333 901369 536222 402508 607693 376251 578614 576619 135526 831042 803229 181359 901944 149112 646534 917681 970401 985044 407876 274215 350223 137583 631096 667843 018967 445410 853158 768610 764466 745244 401771 839046 027049 145337 865140 587883 685655 544443 873736 535421 552234 173033 105539 435882 533302 226041 528425 521544 712829 964945 272942 581542 912640 966727 634170 874503 682483 391530 280556 965151 566773 899692 326379 549230 271719 535691 888232 863880 676186 540970 324637 090411 657161 863223 901403 946849 640520 876002 469835 340942 154571 644772 608289 913908 859226 477892 622836 464320 869987 716571 654752 411778 400292 298611 375881 915232 118617 684575 589275 711967 910448 949831 215367 395286 109545 024986 621103 511227 634737 316602 269231 764975 679117 997970 107910 822398 702920 537929 835231 004646 496078 835007 554296 619156 994045 367291 792409 063126 579732 613064 095363 803759 950178 705824 987776 505840 709384 815604 186597 409372 351258 419479 776026 309665 794512 057530 566126 220396 231048 105184 552330 749721 005808 171755 132351 430123 758618 782978 968335 775619 356429 084873 273945 685725 011887 287113 447780 920650 376669 348364 118465 321798 889415 927196 097667 532062 064726 204202 374169 556121 646102 475197 164241 692190 314707 545498 914020 785028 509680 246896 425272 389269 815482 959948 259983 744068 604301 068166 292879 198717 050246 307169 268783 593098 244875 436284 818437 377891 315325 662972 216039 123860 685966 406343 982983 179633 708200 618875 259784 204855 424991 930200 139387 177513 666334 960636 120825 989467 421208 790272 008908 735221 563565 508507 565255 591953 698396 093413 581797 849105 713561 654173 340880 408510 095375 687328 823131 523185 704237 870349 727458 097877 521422 996821 002243 990599 790234 227684 052797 969724 155551 581182 048941 162590 793039 031271 235384 983741 307701 063957 529808 848871 295001 955422 364340 361919 498238 669000 413106 176524 342027 196281 252850 252472 271987 744728 139755 144369 439315 491837 351358 853482 283092 580559 371841 544250 968250 096837 107801 885749 448353 320502 507133 225135 030100 959799 390870 053266 650423 214389 554512 133318 688646 115495 582794 202365 534798 177916 368707 991988 644340 761243 955572 471932 216347 889237 036091 317254 192912 748823 041695 021288 070676 805407 952995 063875 902405 214569 380149 953464 815775 281193 263784 364061 128992 487019 995858 252992 641568 411804 054071 700888 899776 800314 354977 789560 497003 460831 085450 256952 244880 963841 831727 357360 448354 224075 407313 298137 632116 793700 592856 949498 155544 136517 438488 096407 302904 556812 483903 359124 381381 430383 970221 276317 393569 455982 196879 239450 058870 069544 415939 329978 274629 385719 902576 328578 146105 980906 666957 666186 936237 480299 869343 279205 245948 459170 704236 124892 389094 331678 392406 975490 726442 046018 937081 929611 233528 570452 877445 555804 959787 533455 788208 368960 980337 062819 722666 319075 961286 838986 804885 884134 382247 761211 729394 031177 821310 055603 295473 848720 504620 978243 922385 796837 628709 024835 410163 562751 460214 946361 997521 815850 092861 779141 857139 652250 262235 387798 908050 405307 759953 640082 544188 214086 665008 290722 872973 910780 551621 023476 343950 632916 664993 453023 659487 490587 207743 566484 622709 990721 567600 415014 157563 303739 169124 884966 687013 936551 724375 507802 495183 844346 528674 007241 923931 307932 447867 215352 505480 551809 148399 802891 335346 206719 353965 947920 945074 420783 679091 997031 779963 276547 695235 337095 307128 218513 935694 148596 834972 734978 444430 551366 278960 668503 037288 189857 730687 213879 029345 335107 777916 695876 851538 328847 039779 431469 098367 662839 472875 625510 145545 707073 118946 947129 680783 622210 915058 861616 254387 688627 621430 372226 102465 438557 195133 310304 569627 057257 300262 452345 514080 267730 427436 258168 435430 897638 834404 351178 049922 264919 291699 721153 562364 713739 531252 561556 556703 518495 337207 522457 498618 012234 106410 888752 181229 503876 487483 201337 260131 060798 167120 270923 911402 442573 760282 927573 541957 826948 158635 945280 291418 647843 620168 850325 175654 703637 010405 765776 264168 408241 756638 768955 500958 273727 616093 415799 218943 744422 984485 538253 986400 510564 788826 552808 036051 200136 934020 619493 613814 681562 444915 712724 319432 599938 147094 499479 091380 211766 430479 860641 340732 757554 581602 936424 643255 416760 556249 751990 948094 915057 313883 138627 748512 009093 613191 544086 873649 183992 694373 695201 564000 518144 / 1591 > 323231 [i]
- extracting embedded OOA [i] would yield OOA(323231, 1617, S32, 2, 3181), but