Best Known (101−89, 101, s)-Nets in Base 32
(101−89, 101, 120)-Net over F32 — Constructive and digital
Digital (12, 101, 120)-net over F32, using
- t-expansion [i] based on digital (11, 101, 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
(101−89, 101, 129)-Net over F32 — Digital
Digital (12, 101, 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
(101−89, 101, 1435)-Net over F32 — Upper bound on s (digital)
There is no digital (12, 101, 1436)-net over F32, because
- 1 times m-reduction [i] would yield digital (12, 100, 1436)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32100, 1436, F32, 88) (dual of [1436, 1336, 89]-code), but
- the Johnson bound shows that N ≤ 7 488155 226237 962283 665876 464954 850615 147691 503672 808565 412794 671906 500210 948643 477313 660371 227518 437422 627634 800423 743400 426729 370667 004375 595849 905755 849963 164570 439664 988950 701168 377163 997023 816563 323420 653349 859264 924903 551288 764245 930358 414930 239935 905536 072886 328429 586663 750655 207916 573425 538691 703738 809593 505308 526863 443533 660692 568645 486658 903663 050727 613345 767939 500800 018500 224218 369154 303700 406253 511049 059215 480727 338951 080115 385161 742555 142780 048305 209925 627316 181910 947971 879668 297141 105106 153754 930013 631364 196477 852831 483131 956460 508592 405498 611508 614975 245943 507929 423908 424268 608912 989478 188557 049139 010249 657842 853429 336032 486364 464057 454577 965375 851879 148632 813330 091723 832411 385725 501524 209153 269078 208762 328815 890020 388201 694500 484994 070726 176357 699425 354650 202911 510206 073894 922457 540820 565798 047012 028539 184837 957760 475494 466200 662648 086692 008058 152721 679322 978042 973586 898231 004829 196585 777105 930982 529926 139390 847245 028575 070000 155217 210800 953391 940064 546509 127324 983413 620904 079603 091609 537945 774304 209012 467514 744930 455810 791900 294855 841483 404313 323454 072378 648052 874975 620753 330851 978009 494445 587214 385327 226950 652618 043040 009753 339427 585526 681769 920441 311616 352794 369556 542540 938390 355552 989084 486172 188159 529744 553448 650835 796783 493320 458932 237429 456189 077674 278980 366006 282197 962799 805551 540689 476248 487104 696679 673912 625059 804474 387567 708837 335397 737712 545509 786725 778880 874425 769362 269340 674226 095505 199695 194762 173028 018451 831167 488069 099021 519470 798762 023881 671615 393042 568512 796211 273842 363522 411815 183513 829957 981057 908596 892440 928968 915803 817402 553586 480211 291654 918822 989954 450414 830079 165148 526350 183233 446760 006555 000487 413693 542545 287473 971611 589641 789237 783324 267047 364040 866882 255843 386971 174343 556098 905731 079706 737624 302271 233986 376906 043127 497439 749544 025636 082913 634893 877685 266549 823094 524823 062552 945118 914770 243800 131258 906529 976482 328222 959402 741564 443040 880383 845865 759939 173553 357848 986415 788304 974712 221990 430154 814013 440736 827974 415696 768024 183493 236157 < 321336 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32100, 1436, F32, 88) (dual of [1436, 1336, 89]-code), but
(101−89, 101, 1443)-Net in Base 32 — Upper bound on s
There is no (12, 101, 1444)-net in base 32, because
- 1 times m-reduction [i] would yield (12, 100, 1444)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3 282439 344307 580920 381352 745369 702495 923623 824048 277801 480208 833840 727752 272832 506434 893532 800182 538985 299347 994815 853922 310466 581267 430336 962540 982944 > 32100 [i]