Best Known (14, 14+91, s)-Nets in Base 32
(14, 14+91, 120)-Net over F32 — Constructive and digital
Digital (14, 105, 120)-net over F32, using
- t-expansion [i] based on digital (11, 105, 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
(14, 14+91, 146)-Net over F32 — Digital
Digital (14, 105, 146)-net over F32, using
- net from sequence [i] based on digital (14, 145)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
(14, 14+91, 1684)-Net over F32 — Upper bound on s (digital)
There is no digital (14, 105, 1685)-net over F32, because
- 1 times m-reduction [i] would yield digital (14, 104, 1685)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32104, 1685, F32, 90) (dual of [1685, 1581, 91]-code), but
- the Johnson bound shows that N ≤ 4320 194525 362245 023919 351706 750314 868421 883847 222379 420208 253742 042575 327270 096018 452444 322804 415904 873218 681966 797127 506661 805489 288318 045230 788984 890968 331056 372575 646835 490461 367884 229419 364279 366547 230411 419184 430005 355666 333480 198400 689540 717750 665177 154744 919908 339337 430061 071113 089384 798880 509278 942182 840573 392482 892678 796694 454849 054892 389349 512556 175573 674806 362094 548562 656024 651959 838115 094512 049355 460652 654255 672427 007760 873043 713931 561275 534313 354422 283938 651980 632488 212067 344840 263311 799241 886031 114020 763857 188677 011095 491416 090414 405639 172025 978422 426675 918114 996869 320179 822802 690345 145578 332466 817352 120074 842802 996851 595616 427710 900946 032577 980319 126654 820488 899356 256761 700259 659564 114428 415234 610984 214772 534039 643837 395760 050155 149671 327668 338171 711246 823136 630787 211815 439460 786874 295760 904817 203881 318527 155573 831694 888685 993374 400526 370938 667957 287153 925085 714431 869874 739974 976247 248118 518736 665789 343221 105178 535405 867847 045106 020330 988018 308347 233553 518635 099487 775250 806472 724798 067430 872145 079280 111787 800744 658806 667947 142701 334198 413215 225686 042549 667031 256858 234180 608540 590377 971555 641596 610036 916567 578402 513164 190718 183469 682847 433417 550839 066565 655085 129512 981733 482222 535203 006983 870232 461034 433183 921737 403845 309331 790607 923839 036994 353209 333957 171028 994496 084820 773045 492900 377854 412682 784206 575441 384094 308416 462342 609305 269255 491146 030762 202853 514227 076797 332750 785022 233549 651416 532568 584548 009523 537654 831713 077195 515993 500648 926560 896443 445021 717869 076760 434488 340303 497582 758370 987514 889601 659928 799751 679779 559204 438685 608250 589837 618804 444037 693902 251207 328641 296950 816468 308650 023640 464773 787208 237980 926498 144735 440077 521323 375034 876145 868532 262080 628785 342145 329740 177969 321512 697936 065091 786819 636716 398539 702242 013380 358189 914983 971987 581059 755367 488566 182907 565607 491480 809114 304344 186016 318497 790081 193928 039691 912328 286642 624126 810891 747012 657367 905662 043656 055990 704037 634142 049593 643590 793017 141318 792243 547193 982656 017326 531542 328956 299386 461589 757510 299678 795946 862946 777940 971277 028284 173158 495365 299354 509843 475211 501955 705148 226704 863711 161275 357752 370309 266921 402923 370941 965004 051174 864755 887118 797836 712950 839883 280116 696451 077709 645540 610103 548586 851963 388352 645674 620751 173721 140609 476572 378821 173493 274514 767889 531465 624082 732114 022016 520741 973204 385578 799340 800840 185731 354052 578666 891432 178399 767626 083430 < 321581 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32104, 1685, F32, 90) (dual of [1685, 1581, 91]-code), but
(14, 14+91, 1688)-Net in Base 32 — Upper bound on s
There is no (14, 105, 1689)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 104, 1689)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3 511627 338866 801775 792298 323833 603921 373962 280503 619884 898177 035510 373617 844599 728565 275577 604613 584267 816094 209962 467040 489462 727333 271009 332279 228690 118976 > 32104 [i]