Best Known (12, 109, s)-Nets in Base 32
(12, 109, 120)-Net over F32 — Constructive and digital
Digital (12, 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
(12, 109, 129)-Net over F32 — Digital
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
(12, 109, 1434)-Net over F32 — Upper bound on s (digital)
There is no digital (12, 109, 1435)-net over F32, because
- 7 times m-reduction [i] would yield digital (12, 102, 1435)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32102, 1435, F32, 90) (dual of [1435, 1333, 91]-code), but
- the Johnson bound shows that N ≤ 230 744295 237102 175256 300748 686082 801979 285229 721260 314759 500622 474889 047538 113997 581744 609474 273075 072291 457471 347363 355895 421944 060179 205300 428299 502102 246749 754081 245230 104381 156743 650414 275368 045255 109037 543387 451754 892425 519757 337214 483286 579811 830262 866657 292822 915595 978675 519800 209677 077870 749446 288488 986440 243642 523501 119066 299392 743401 616687 486682 940951 467628 991585 041524 553516 073023 401792 092475 019064 009459 106331 813323 496112 598982 793383 422734 360308 774776 619040 369587 918869 155827 665561 726736 770363 562565 350462 415559 257322 785985 484656 242114 345801 309358 637574 474295 609445 373878 376752 595447 195490 836287 224076 706069 587088 203790 209687 202542 921830 730788 482351 880395 206119 275706 459285 367496 608916 620230 518053 580974 083923 730281 213112 467784 914793 086526 769542 150791 342655 155757 855099 477958 982421 418799 132723 946540 501789 987254 584975 275919 056138 886075 384517 109051 495775 646259 935108 697507 062535 929760 259650 617826 294427 634950 335336 692153 341373 368037 915458 223823 902978 182525 546434 490410 862901 842882 939416 282533 099494 948490 679438 301271 120617 717598 517369 089603 701336 073593 775998 510361 356199 133463 480383 190597 176789 190061 140752 755567 028055 504961 746047 353031 840800 102721 633516 652328 919493 213731 580144 046818 885880 445727 577551 170047 049475 258453 753637 959359 158244 226294 544260 492712 874179 026630 406788 696957 910964 026514 878061 360911 472466 892789 924867 880040 623600 169001 084630 934260 650466 126584 624423 702078 335009 542140 325336 651989 052719 712901 034027 004626 406984 441834 313844 291198 785398 971032 325418 591779 007322 364991 390723 729138 450599 215707 231619 807060 309195 267770 420801 824953 707887 141830 009575 138920 365883 266519 653049 756002 610454 047354 344000 802978 223131 368710 950859 176387 007370 734790 942380 207613 468160 109198 385570 773360 972046 368148 665191 569849 612345 836256 370681 540002 836839 243242 968803 140059 328545 522506 242801 112198 221091 680671 969628 221539 889889 135360 949862 034952 396442 756376 965194 697385 472415 302796 935768 398213 052821 291671 032799 453803 457822 421344 241186 569666 351048 463858 152891 441334 589920 673077 450947 552869 519551 858594 016141 < 321333 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32102, 1435, F32, 90) (dual of [1435, 1333, 91]-code), but
(12, 109, 1443)-Net in Base 32 — Upper bound on s
There is no (12, 109, 1444)-net in base 32, because
- 7 times m-reduction [i] would yield (12, 102, 1444)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3371 113242 975192 558575 952914 297817 288959 606698 338294 782455 533611 787549 576234 426055 692728 757932 175643 230896 656428 048956 972210 900101 646850 886789 315121 558048 > 32102 [i]