Best Known (12, 12+82, s)-Nets in Base 32
(12, 12+82, 120)-Net over F32 — Constructive and digital
Digital (12, 94, 120)-net over F32, using
- t-expansion [i] based on digital (11, 94, 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, 12+82, 129)-Net over F32 — Digital
Digital (12, 94, 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, 12+82, 1447)-Net over F32 — Upper bound on s (digital)
There is no digital (12, 94, 1448)-net over F32, because
- extracting embedded orthogonal array [i] would yield linear OA(3294, 1448, F32, 82) (dual of [1448, 1354, 83]-code), but
- the Johnson bound shows that N ≤ 9277 616511 331322 344841 959012 568661 535018 757971 406565 246862 396432 749661 935491 007122 700148 344586 320968 061313 255802 415011 906412 653966 432302 606662 482916 971644 900462 112603 210931 971275 049717 700965 446559 517871 819902 517306 671352 502131 617481 922212 405796 053665 733308 902759 407765 099184 371500 307180 611405 573965 121606 830572 671127 557207 971437 081135 695946 106977 085261 978957 424294 007539 777581 024848 646748 374218 117585 422599 658835 685301 437777 703383 168818 294528 380704 894552 219421 398903 910186 560436 165107 317250 214769 710932 127697 008232 805665 050264 225976 874051 207453 707878 689862 573293 734552 028907 152313 418377 916911 968557 545912 496420 394537 738066 564542 480704 436800 481723 786164 448517 914515 985173 497217 333753 750434 784720 564598 612508 491732 170290 453475 894393 493086 753535 475962 208087 792919 942708 868086 400211 652081 575896 173043 688091 346643 456686 321441 069030 687009 649283 967674 323499 288059 480732 418109 829732 254760 358019 241453 803341 408864 187764 330093 990562 691553 553932 419732 568855 832081 432058 414823 331036 534500 408450 414428 248230 532558 344845 653648 455930 014691 712629 176172 352156 096114 712345 366023 982697 706525 757408 956723 317583 434835 677553 300865 832727 184773 227198 566924 071039 877035 098678 173201 417648 731840 368983 390931 631552 217484 343299 731022 837000 410288 843754 135847 831346 023489 174497 800104 926656 196965 238180 144486 577446 085744 063489 279713 339725 861676 555776 346242 435071 109470 005279 277557 669929 088627 701169 339875 480899 423706 479728 858101 946653 829489 524479 856557 547751 670011 793006 329719 603478 807020 380118 629712 825053 381594 215807 566208 022924 509485 939860 273472 886222 652524 160955 683680 970471 028264 069897 684046 590353 275419 429098 097553 300014 543005 578097 127863 834281 745244 350485 719852 168409 534480 381454 527427 383942 873715 929231 870211 485216 423382 137058 850671 237557 263848 755368 492987 546527 352069 596207 577138 619646 488637 276186 842012 097782 032142 082373 481319 958485 701857 889581 518510 087698 497394 491048 846274 324780 207820 641533 842594 467548 937259 335602 295164 350684 134742 758980 549925 209858 381807 245768 592390 523663 424501 961908 609921 190488 743716 684804 009332 441101 100063 517753 179397 719246 290486 983290 < 321354 [i]
(12, 12+82, 1448)-Net in Base 32 — Upper bound on s
There is no (12, 94, 1449)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3051 538204 787807 584848 496659 264809 350579 548410 229674 061251 795171 948607 633052 177471 653512 591127 934095 559316 652435 566296 744663 709927 235261 657120 > 3294 [i]