Best Known (44, 44+∞, s)-Nets in Base 16
(44, 44+∞, 225)-Net over F16 — Constructive and digital
Digital (44, m, 225)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 224)-sequence over F16, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
(44, 44+∞, 226)-Net over F16 — Digital
Digital (44, m, 226)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 225)-sequence over F16, using
- t-expansion [i] based on digital (43, 225)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 43 and N(F) ≥ 226, using
- t-expansion [i] based on digital (43, 225)-sequence over F16, using
(44, 44+∞, 697)-Net in Base 16 — Upper bound on s
There is no (44, m, 698)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (44, 1393, 698)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161393, 698, S16, 2, 1349), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 34934 603812 656868 671643 717234 814320 473774 877566 126304 299021 333517 697113 049146 933432 928053 735955 678477 541598 075734 119879 220609 735028 797411 633985 216359 608428 441492 443250 974288 391661 143425 118290 433690 429480 223233 763085 402178 709753 720587 705871 756702 674086 043585 677872 188397 389550 631445 202796 734829 448995 460500 495124 270751 483567 659181 242288 821999 445618 775669 761885 977743 837986 676936 465325 837338 355558 481155 142690 547512 493462 433894 579589 178949 707073 046197 008368 780056 718898 738051 744440 647964 154424 723012 023449 662830 498386 369695 166612 025140 275807 699908 901043 691787 767443 597874 190584 335610 955166 600685 678895 732058 497795 561336 957083 491809 265210 102056 596987 674354 721221 382333 770475 190237 988180 306555 953085 675827 185270 356847 618933 509870 616672 257771 083542 407494 410399 246649 973835 460648 636639 530213 451721 566730 895078 142170 663850 640433 544417 906759 141889 998926 877139 041561 871135 414403 664937 870018 341916 845510 631985 998396 590511 717577 853591 914782 236107 576648 455146 404726 096149 759244 490257 706696 708387 048458 316183 098402 190705 189305 622544 004703 029569 152105 441321 773544 148735 107781 422237 539074 119505 349405 972623 176599 738422 713373 639555 431588 731637 089912 234208 634704 075928 539981 384135 173284 472581 061247 748511 696747 646261 552051 994979 763800 396370 590173 619090 154476 565607 523696 835186 248376 988350 912457 384414 850248 355828 013914 861189 636145 441824 099493 794603 106527 264640 285112 416526 887770 613681 116433 653354 674373 499581 724724 680288 742918 373947 518796 211422 569551 433140 118786 935837 381896 279409 009695 358326 525490 501592 688166 409857 312390 920161 186929 334274 813904 922146 513501 435508 198946 336281 302481 819635 732789 805643 371604 184728 698184 060743 082211 542783 177395 735833 903942 600101 665827 172367 224726 943778 742401 499136 / 15 > 161393 [i]
- extracting embedded OOA [i] would yield OOA(161393, 698, S16, 2, 1349), but