Best Known (109−96, 109, s)-Nets in Base 32
(109−96, 109, 120)-Net over F32 — Constructive and digital
Digital (13, 109, 120)-net over F32, using
- t-expansion [i] based on digital (11, 109, 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
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(109−96, 109, 129)-Net over F32 — Digital
Digital (13, 109, 129)-net over F32, using
- t-expansion [i] based on digital (12, 109, 129)-net over F32, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 12 and N(F) ≥ 129, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
(109−96, 109, 1548)-Net over F32 — Upper bound on s (digital)
There is no digital (13, 109, 1549)-net over F32, because
- 2 times m-reduction [i] would yield digital (13, 107, 1549)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32107, 1549, F32, 94) (dual of [1549, 1442, 95]-code), but
- the Johnson bound shows that N ≤ 26556 299273 077039 480000 122629 962020 353716 893860 905267 886123 689067 959531 176853 287453 587328 242521 252123 510225 171051 748177 445007 556533 881270 020215 355481 631933 578993 724229 831797 419386 950474 345706 696527 069237 914008 278356 386160 157487 731724 633286 637429 491197 231916 469541 928520 008938 048338 094279 340536 525961 593336 212019 487670 640871 681681 569072 689509 353133 917383 125623 781151 925361 722712 058985 935043 149696 295995 083657 859405 139826 260007 821701 032012 493957 035304 865154 756470 078099 016593 226584 765395 236827 660908 208339 276158 462711 195185 436752 565419 203846 187136 886568 591509 055088 991565 268743 993990 310899 564665 388256 571161 767254 885856 162312 954557 573623 379530 816265 974084 347203 740138 882674 170619 387861 587220 018463 603988 048892 258554 857531 420564 841028 488835 274368 943686 772981 914984 891774 926497 629850 990115 868067 690813 759238 555419 094341 897059 591445 363856 844589 404566 148722 524278 418895 400694 981107 633389 044237 076589 917176 749847 317010 866518 528022 936162 791050 846988 487104 007842 198235 253693 156259 427515 806097 642270 816220 359375 706785 931114 460807 888140 686291 759894 250277 393311 779246 852870 639497 244806 396183 764079 819506 727921 167515 644291 033636 193223 038983 510898 062422 188981 882199 293695 570354 401542 703881 249723 800105 950597 750155 062066 553313 285678 350456 092157 689273 645898 840134 913479 611415 773022 877362 059429 435601 101325 786199 859686 672523 125809 853721 586994 657207 717695 483885 791696 239370 622288 573663 296235 512602 643794 989594 000111 592384 625553 110218 980905 827114 522045 874949 558763 370894 317266 814828 525173 587687 522777 255678 348237 714123 576815 850430 291735 342634 165991 507367 222127 880803 029409 312398 383407 845283 517185 069722 748379 305422 166465 472223 657048 650032 223347 900041 205076 335645 120901 583181 162220 316814 544207 125462 855929 388008 704944 322413 054451 914730 625669 778438 921722 651085 297837 034400 654245 043734 354384 028070 989293 354541 357335 957611 318374 657788 725088 287404 694037 549944 064696 762596 595159 491924 729738 761280 947006 088306 450437 944664 268933 068173 774715 820765 061963 023328 398184 553228 867070 283995 997079 244929 053974 960673 628525 607982 942559 629413 851703 896949 340711 230404 925092 483371 538803 770513 646498 861722 658006 454755 659631 925682 214299 765838 220273 822174 529409 341656 475480 240277 933944 410011 263400 317856 911095 032180 < 321442 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32107, 1549, F32, 94) (dual of [1549, 1442, 95]-code), but
(109−96, 109, 1557)-Net in Base 32 — Upper bound on s
There is no (13, 109, 1558)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 116 430307 153431 398449 913441 890918 640433 649097 801014 500844 513929 487784 501601 899904 955680 842911 737202 628175 230248 791805 426834 968816 886721 462127 707338 172862 133502 611696 > 32109 [i]