Best Known (11, 11+81, s)-Nets in Base 32
(11, 11+81, 120)-Net over F32 — Constructive and digital
Digital (11, 92, 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
(11, 11+81, 1325)-Net over F32 — Upper bound on s (digital)
There is no digital (11, 92, 1326)-net over F32, because
- 1 times m-reduction [i] would yield digital (11, 91, 1326)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3291, 1326, F32, 80) (dual of [1326, 1235, 81]-code), but
- the Johnson bound shows that N ≤ 72291 728984 188819 042366 346805 492581 865518 839712 118166 873768 681225 580540 907570 415939 299217 851126 012927 334502 285391 338441 788435 313351 446385 787830 150343 360475 763503 579159 808539 324260 536653 543858 727963 549892 427308 402761 609048 164604 645956 452739 176102 699674 023600 787170 119939 047122 850321 511223 770073 889782 716394 174253 904381 359627 856049 425100 868206 502596 877958 657943 909417 619123 192464 400798 974925 298216 559943 412237 131708 232289 011617 330484 220808 690470 191345 183181 356546 685562 623492 299343 252437 607469 765515 658558 145719 210608 302183 089801 213378 862260 591695 508900 077408 622170 916861 010189 972556 797314 482352 466716 664979 314671 010509 120602 307591 060754 605653 260603 561983 365364 353567 424384 255230 330451 133835 839132 076916 977185 085061 403742 193404 600446 670148 957404 918553 776560 320590 248586 131400 986737 677650 805228 861655 791165 297430 555206 841381 298379 377309 111255 321532 312820 336612 000649 253436 592961 288263 526223 177943 268766 506331 195903 736044 291221 130381 576358 879768 398016 463686 269382 449974 819937 331494 041643 858963 126262 655916 530619 565139 994042 200420 729824 688236 106899 357895 621416 937181 064621 625783 340150 667533 672813 432038 278362 968611 276609 629833 368636 037232 317257 934953 693549 918252 119800 521044 761780 051208 175875 510731 077259 747775 000780 267303 997425 588436 610820 632080 066324 390102 174464 449856 384595 614640 238473 313981 717886 584296 106187 098934 921657 303386 098322 885523 784039 738973 883134 998695 387636 565534 250540 183045 721537 182220 887520 310349 883473 613576 323956 706210 638169 158749 859490 778627 330009 218636 284235 453367 915690 185524 543377 809863 287379 323030 351270 610535 023198 486765 141143 364299 112343 557762 313738 386872 023185 636418 322106 990458 733866 258324 096184 600287 708643 329954 170674 914325 542256 205003 406177 644596 419928 532988 772998 187342 163265 897289 748518 240398 526751 459905 102683 165155 588891 493124 374748 909209 433332 599688 491390 967356 958030 913451 258250 196048 606570 191971 613064 437485 988938 340319 591954 < 321235 [i]
- extracting embedded orthogonal array [i] would yield linear OA(3291, 1326, F32, 80) (dual of [1326, 1235, 81]-code), but
(11, 11+81, 1330)-Net in Base 32 — Upper bound on s
There is no (11, 92, 1331)-net in base 32, because
- 1 times m-reduction [i] would yield (11, 91, 1331)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 95130 126509 118909 587172 397683 385331 574537 297991 176879 543646 663331 275265 813153 443137 910395 177241 072235 634108 116932 894571 157833 338971 001770 > 3291 [i]