Best Known (10, 10+90, s)-Nets in Base 32
(10, 10+90, 104)-Net over F32 — Constructive and digital
Digital (10, 100, 104)-net over F32, using
- t-expansion [i] based on digital (9, 100, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
(10, 10+90, 113)-Net over F32 — Digital
Digital (10, 100, 113)-net over F32, using
- net from sequence [i] based on digital (10, 112)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 10 and N(F) ≥ 113, using
(10, 10+90, 1210)-Net over F32 — Upper bound on s (digital)
There is no digital (10, 100, 1211)-net over F32, because
- 12 times m-reduction [i] would yield digital (10, 88, 1211)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3288, 1211, F32, 78) (dual of [1211, 1123, 79]-code), but
- the Johnson bound shows that N ≤ 18874 665979 223468 173060 024731 847620 255607 755011 505523 931510 793452 365995 738493 515058 552391 345500 076143 413006 940477 569266 457705 430524 014085 573858 567112 896693 298978 632985 602382 967310 289927 326648 906096 274059 789776 757219 973016 100253 747132 539539 637446 492990 079705 004040 094321 455081 226680 643950 210262 881960 577520 463582 867273 859480 977638 767310 327153 899026 336021 345363 973447 339216 778463 190129 054370 419301 297228 460989 732604 275165 916404 610530 960295 397276 035705 227845 807676 116851 869881 842583 458861 594580 524828 037178 568996 799302 505604 726447 168482 947105 274455 928992 205295 886067 448205 674922 775831 136513 484547 374975 447106 430901 241329 776762 035699 970891 401538 526032 218555 153022 217913 419782 155312 414662 181759 751411 853479 806045 943687 314179 973456 169441 329014 156806 620031 802040 280923 134656 364457 524934 347164 059509 314209 093621 578744 074454 370530 875106 815868 694331 083832 437452 965522 041796 740996 088915 638890 254653 474189 391978 759861 686839 010883 859445 079863 346515 766238 494485 549905 571972 141810 762793 160228 861105 655019 739573 107238 205572 429940 991966 236587 120247 795601 913234 116534 593451 696117 861156 004232 616010 001661 435070 229048 338718 472070 389009 304906 563881 829030 708356 436805 134516 086005 311794 761612 374121 959010 911526 556090 272264 622714 247188 636839 060015 380090 129985 776471 753863 961247 825727 566017 785381 758482 793670 172535 742434 514928 671386 113897 078872 142363 425764 786912 663348 516220 943082 665728 661654 703166 555467 305844 145427 384484 652099 222125 007537 191936 427611 346349 964714 024591 626570 330309 758817 007672 993216 019431 017026 007322 529219 865135 608743 065148 487862 112933 156813 617690 779145 916499 875096 647129 423222 977814 585773 194199 724501 768468 097225 464615 947993 107697 736215 228830 059217 103298 097082 128663 795658 053278 542011 865013 947530 < 321123 [i]
- extracting embedded orthogonal array [i] would yield linear OA(3288, 1211, F32, 78) (dual of [1211, 1123, 79]-code), but
(10, 10+90, 1215)-Net in Base 32 — Upper bound on s
There is no (10, 100, 1216)-net in base 32, because
- 14 times m-reduction [i] would yield (10, 86, 1216)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2788 457517 517364 690287 917781 539104 413664 585305 490732 729576 662270 752131 654085 747082 911834 990618 546821 518552 918097 088049 149842 920615 > 3286 [i]