Best Known (102−89, 102, s)-Nets in Base 32
(102−89, 102, 120)-Net over F32 — Constructive and digital
Digital (13, 102, 120)-net over F32, using
- t-expansion [i] based on digital (11, 102, 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
(102−89, 102, 129)-Net over F32 — Digital
Digital (13, 102, 129)-net over F32, using
- t-expansion [i] based on digital (12, 102, 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
(102−89, 102, 1558)-Net over F32 — Upper bound on s (digital)
There is no digital (13, 102, 1559)-net over F32, because
- 1 times m-reduction [i] would yield digital (13, 101, 1559)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32101, 1559, F32, 88) (dual of [1559, 1458, 89]-code), but
- the Johnson bound shows that N ≤ 31708 384123 370112 206321 825204 999030 150001 204594 679237 770656 050722 596496 479745 209575 182857 700628 302425 378653 490163 305609 081288 332874 622835 869519 589891 876085 639764 424298 015213 911360 466207 213234 916096 301529 879360 363361 403293 590045 807530 996609 009562 338661 609927 876747 533153 029077 531668 538088 646485 675331 206896 090950 965825 796039 219104 985600 437629 102161 569441 874863 327496 875645 525863 212539 978511 684473 948393 771649 061373 796240 074211 601660 791255 027113 277643 329183 961043 159563 033065 982912 023284 591656 482634 471745 765496 706974 248948 427668 868928 037825 660153 263508 021479 025212 250556 520961 126223 453799 264315 305018 644637 664234 883281 929894 296335 281438 529984 089641 323126 772445 571655 825225 774895 036048 343609 924313 090005 830311 222749 209215 569353 258664 104649 311868 623055 693143 361850 666741 349185 452692 931579 624502 621740 566473 408115 762178 269960 140174 534742 728094 540228 452052 951920 336843 465148 993952 814128 138693 369101 276758 514062 598027 829690 332367 015289 286034 896229 097461 402894 590609 354172 399593 788675 516197 515350 695363 926906 493669 753444 696099 031520 931254 326740 577858 186084 976655 266340 511411 113363 403847 681811 343064 930359 374270 025369 640963 988640 445556 392022 482818 379426 822132 125123 622184 028574 188380 684196 893360 237517 088862 454672 530889 447855 512943 483716 254040 723770 271556 315428 600766 226530 044721 492306 521349 330847 772464 756394 181887 638163 814525 793432 575456 323337 671111 067360 251651 142719 563232 478262 407031 410414 551684 391703 772742 881126 621267 245830 054723 213156 070129 627025 959729 670347 417382 479518 225361 529061 945617 231991 006260 041724 835912 681559 157552 358920 219788 465421 629807 902403 025171 041691 094190 390898 259723 141991 468051 587129 447124 291373 088494 095813 975802 393173 302736 483172 592529 580438 312037 562763 403920 149138 362842 150707 023697 168491 467573 168067 626594 855955 107819 952454 208156 173909 029370 162225 169380 924587 938293 363848 263248 852693 813030 108073 481645 952751 336140 707395 056493 099320 985345 151748 978717 319309 810269 451128 363604 885257 659288 850072 470072 168800 691080 418116 256349 055776 497964 614760 678808 794044 179323 861149 317680 231013 444247 325342 270175 732078 847513 943743 168951 461219 782549 622268 076151 719566 476710 593328 194819 636443 067789 920567 658532 586706 272520 905867 645659 273012 531488 645573 162695 273266 603505 995602 818681 204465 463758 < 321458 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32101, 1559, F32, 88) (dual of [1559, 1458, 89]-code), but
(102−89, 102, 1564)-Net in Base 32 — Upper bound on s
There is no (13, 102, 1565)-net in base 32, because
- 1 times m-reduction [i] would yield (13, 101, 1565)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 107 378926 531700 534128 446570 027909 740953 661970 327260 875672 223261 851512 696578 140278 889850 131196 263698 901280 160988 591461 704245 943801 470524 161791 453069 383952 > 32101 [i]