Best Known (11, 110, s)-Nets in Base 32
(11, 110, 120)-Net over F32 — Constructive and digital
Digital (11, 110, 120)-net over F32, using
- net from sequence [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
(11, 110, 1322)-Net over F32 — Upper bound on s (digital)
There is no digital (11, 110, 1323)-net over F32, because
- 15 times m-reduction [i] would yield digital (11, 95, 1323)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3295, 1323, F32, 84) (dual of [1323, 1228, 85]-code), but
- the Johnson bound shows that N ≤ 2 055674 174438 605250 694094 877348 043527 624550 675644 026477 566577 559752 421774 439661 150462 999884 406050 322955 113966 887424 457390 018553 729394 419801 296944 437936 031808 507833 530203 657219 864983 128004 695145 141769 885787 057345 277722 910574 754385 911574 332904 932022 388786 516558 741422 079824 772142 887919 456183 720013 159808 586672 878106 820447 558208 367477 709271 007732 828997 173848 542685 740472 867865 136964 618810 247686 195193 007199 656245 593095 558350 854717 752400 354844 120683 023528 296116 551870 705352 544145 764605 140606 119698 178704 736038 867080 697086 828783 619648 657535 783461 742396 657884 585018 123990 755094 506934 877957 489257 395640 245452 117728 110680 475781 266315 721720 241457 531643 531713 620457 595006 679719 352458 838422 197168 818777 953619 929449 789914 713083 713895 090091 559088 314353 714429 717760 713128 841456 837362 715040 611295 176471 953787 383659 084384 311018 159732 069104 206187 939382 777796 912280 279077 083538 376968 531465 206843 375206 044066 421841 935132 643467 029416 530920 923739 356159 597234 793896 988834 847027 074073 631892 518336 247329 571089 309823 838668 662511 107753 263378 304751 250559 976410 048036 297929 270361 947235 634649 881614 620433 362511 742647 506965 966103 069798 924401 228621 585037 500775 520032 826650 714671 596916 689825 861957 703235 061398 674187 149744 633501 696950 881088 036056 498918 658323 280187 374919 623602 578619 531713 379989 922688 145416 317183 368771 509691 335785 110938 648851 219886 954467 426527 612561 705825 589265 296031 637381 890026 730723 630695 716032 646639 531813 823449 120919 735183 431614 395690 487248 134585 808628 970812 027016 568049 460558 388054 393542 538030 207599 923299 875505 225282 397515 708011 180473 191220 301929 174583 849432 949778 416180 288816 996214 786208 606316 235382 539738 054644 712634 044095 050263 790721 121820 067682 665987 664664 684137 794945 689052 555224 643437 501958 375133 180365 718244 929566 794927 873737 600353 633219 992658 979358 174101 271134 218585 984908 356959 377904 487322 569254 620245 645161 020202 432652 438644 263082 300204 177953 668001 < 321228 [i]
- extracting embedded orthogonal array [i] would yield linear OA(3295, 1323, F32, 84) (dual of [1323, 1228, 85]-code), but
(11, 110, 1329)-Net in Base 32 — Upper bound on s
There is no (11, 110, 1330)-net in base 32, because
- 17 times m-reduction [i] would yield (11, 93, 1330)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 95 846156 266019 285958 321988 908185 849659 437863 894065 682369 965289 655081 262640 209633 257196 410857 680716 988438 580290 716178 546063 769586 685826 858910 > 3293 [i]