Best Known (12, 12+85, s)-Nets in Base 32
(12, 12+85, 120)-Net over F32 — Constructive and digital
Digital (12, 97, 120)-net over F32, using
- t-expansion [i] based on digital (11, 97, 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+85, 129)-Net over F32 — Digital
Digital (12, 97, 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+85, 1441)-Net over F32 — Upper bound on s (digital)
There is no digital (12, 97, 1442)-net over F32, because
- 1 times m-reduction [i] would yield digital (12, 96, 1442)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3296, 1442, F32, 84) (dual of [1442, 1346, 85]-code), but
- the Johnson bound shows that N ≤ 8393 086393 354033 616393 809848 677490 165908 764940 501831 362507 579329 034847 871980 798914 436762 426591 231103 741514 747338 545831 855471 729879 287977 201652 597382 480495 558928 629321 840910 967672 646929 189644 366643 418740 436583 035771 695128 411671 762930 363730 447815 993110 016529 833497 002269 950385 130031 381254 970307 197529 923401 034085 360823 484321 139333 378650 598444 870199 608355 207706 243061 519234 566328 639511 986724 418155 343278 468493 346923 608704 117477 086217 344818 052840 962678 525543 444149 058776 744970 375343 238873 591786 754856 716786 520544 493437 624670 761686 377529 613568 922686 202228 497725 099367 647719 087256 238811 920201 998346 250918 993444 047113 044822 900205 038511 265265 942304 697109 721061 789282 184409 821265 101649 264548 370425 758067 107231 940583 857275 102357 361582 004945 753874 238213 667505 653423 899494 501096 087217 019751 500695 376382 765835 388999 979053 109243 089765 154537 112890 313024 614756 125052 943652 678217 675199 035865 066948 040884 106205 371357 120172 200062 707502 948720 098224 265979 038795 498167 939625 835915 795015 509288 694782 519078 528837 028479 578948 405005 518027 927422 628747 265845 172463 589854 322899 068478 271785 137331 232435 693767 971555 242363 688926 704117 035461 849927 965685 738078 734036 607480 445787 736812 261380 734442 127493 766700 951256 944085 460441 127011 577680 519860 762123 448995 013037 726896 759014 798904 785413 892618 402820 499805 260653 992547 129417 064290 345765 125859 258026 072426 741765 405833 866044 953067 108277 402248 839019 961930 565237 423845 607770 073769 856335 171136 900835 386039 202195 694457 801911 592362 491977 310828 590338 162194 007336 909695 328011 766983 000396 246748 429389 963114 266708 055105 281578 595876 449517 658795 308443 976972 115200 569431 814339 075523 275571 256225 599379 434047 110689 331147 801533 857025 976761 831474 210762 182328 919645 726042 230074 042805 991531 929729 619229 030188 022437 031361 492270 040154 684059 566992 630540 273196 912862 321235 169317 666674 316774 955664 069261 168063 836127 255938 233858 360070 684750 557352 581019 866036 534160 904152 197088 220670 843168 571994 099360 589530 904934 902365 188011 150085 014946 167659 143274 842227 237003 555687 583422 941135 572027 752235 392640 742727 671082 908013 790577 444236 342578 856510 < 321346 [i]
- extracting embedded orthogonal array [i] would yield linear OA(3296, 1442, F32, 84) (dual of [1442, 1346, 85]-code), but
(12, 12+85, 1446)-Net in Base 32 — Upper bound on s
There is no (12, 97, 1447)-net in base 32, because
- 1 times m-reduction [i] would yield (12, 96, 1447)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3 175152 870778 756089 913903 696366 283658 614595 881466 146312 286237 227790 383295 466085 806337 281647 611277 430428 461533 039587 269671 906792 209866 735992 389072 > 3296 [i]