Best Known (15, 107, s)-Nets in Base 32
(15, 107, 120)-Net over F32 — Constructive and digital
Digital (15, 107, 120)-net over F32, using
- t-expansion [i] based on digital (11, 107, 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
(15, 107, 158)-Net over F32 — Digital
Digital (15, 107, 158)-net over F32, using
- net from sequence [i] based on digital (15, 157)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
(15, 107, 1815)-Net over F32 — Upper bound on s (digital)
There is no digital (15, 107, 1816)-net over F32, because
- extracting embedded orthogonal array [i] would yield linear OA(32107, 1816, F32, 92) (dual of [1816, 1709, 93]-code), but
- the Johnson bound shows that N ≤ 19867 620763 626587 634090 079818 528944 584782 342744 176336 924029 414002 875615 457957 313742 446973 365441 649381 971710 587321 131091 996317 293116 129605 064190 149609 685097 808697 920461 113102 497498 874787 670868 260613 793464 537594 070590 923932 278535 286895 246914 535967 740471 255939 622685 422359 375659 516911 524713 258781 509745 175291 846966 792969 446327 018595 873071 449722 425058 505267 597654 255313 735986 613366 843750 350552 375856 115302 126798 327722 221849 633970 199131 096141 027545 964000 553188 953651 395688 748113 092572 520159 251056 516091 555296 534175 242866 274695 140383 114825 612664 214409 895481 240288 302847 665653 607392 861612 281831 036010 442996 509788 755599 282648 641150 328323 132690 513278 945897 178992 789177 441131 917146 766338 183993 854741 115614 908307 808459 097775 561556 904627 309690 495370 118495 572616 154661 753732 643228 571327 327989 563162 416106 380101 673580 511165 832684 749370 351573 408349 236647 123547 960018 385427 838711 364163 933159 101371 465281 751106 572576 659024 112277 066979 194808 850626 724871 201582 927308 723135 173149 103974 676524 483293 166868 539210 041456 790802 770364 533276 107699 831532 695992 821060 467971 658148 360603 276003 087079 126806 523609 842636 113144 195209 269162 345538 418209 209959 096561 079233 263101 724982 914610 014320 659892 308334 597063 886412 184113 058882 818961 294477 461092 928344 102979 714432 576669 194981 754518 778838 449785 849846 023928 165196 016713 040321 899127 348470 396218 278170 453431 303622 802630 080051 485516 002445 276981 826526 249175 469883 158480 307609 795730 034147 939503 960901 385827 642520 466307 913974 687228 026844 009738 488121 981773 823723 159531 587904 127273 037653 532393 708695 521574 927986 954390 267827 478638 078575 007073 250958 905094 653939 450199 320572 797033 225842 142393 098658 988350 973607 072076 701341 851946 375593 138356 825538 760203 988198 974037 235983 970039 222704 710219 770908 975612 410628 613138 373191 628303 364615 308242 849009 403163 781150 395007 325304 394218 113377 346801 542676 730894 604217 335348 978309 927758 725718 322435 909554 555488 920176 533847 992591 128976 806709 523492 905079 373613 140046 746283 283295 254256 556768 071138 207401 314980 694058 940713 607324 503999 497735 562469 956939 977501 427534 435781 413487 708011 073241 575089 888391 628323 326817 250583 821504 425284 783820 066712 501900 492818 813292 024651 130114 457557 629550 992378 017002 550764 696973 839239 793227 067100 436369 259820 476594 780473 037496 237677 612121 146386 149047 394506 168042 492080 650605 114039 744608 584799 939085 466831 600218 196118 175914 115484 456488 787968 622067 568919 352266 954995 914751 372060 239071 062762 475553 387609 151283 254270 532262 793544 878351 675253 253310 118621 262421 696717 865778 802779 576331 301924 168782 519715 589054 606586 975142 177606 147274 247977 473852 607442 299713 960822 333120 431411 199430 622248 555569 747713 267487 904301 133912 < 321709 [i]
(15, 107, 1816)-Net in Base 32 — Upper bound on s
There is no (15, 107, 1817)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 113147 910835 526684 624932 208656 172508 300383 824594 382592 540319 085426 335548 721767 363899 564499 386000 178224 038923 700800 950404 822340 448069 684919 681091 893556 624042 942784 > 32107 [i]