Best Known (45, 45+∞, s)-Nets in Base 16
(45, 45+∞, 225)-Net over F16 — Constructive and digital
Digital (45, m, 225)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (45, 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
(45, 45+∞, 242)-Net over F16 — Digital
Digital (45, m, 242)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (45, 241)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 45 and N(F) ≥ 242, using
(45, 45+∞, 712)-Net in Base 16 — Upper bound on s
There is no (45, m, 713)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (45, 1423, 713)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161423, 713, S16, 2, 1378), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 132808 753439 979349 005729 626970 755565 601815 929741 474416 808176 449240 877929 744762 134829 802430 402843 427417 276658 939885 155833 206956 314707 939445 036045 557852 301652 784490 844749 735246 278241 462149 830920 659023 487316 715559 503111 772879 320843 392284 756669 736053 169179 199995 606021 115481 724018 744577 445994 088703 878179 541885 201202 035487 738333 240918 195308 123987 181250 056077 087947 431921 968686 422445 092993 663631 491855 229649 395842 223636 300032 892419 015884 685935 353550 172758 144743 320439 981786 830441 262308 798840 993526 451045 230514 000325 802556 965636 606002 425260 049965 656098 620936 851310 630697 959763 896546 694241 852024 686870 958136 823761 599774 986473 338637 506295 102528 288603 290482 642979 001347 648347 058498 248000 626854 065271 990046 939725 223686 035182 397545 143121 335341 520039 621421 049278 409531 645417 168138 071011 404745 075722 357772 970500 311009 115203 158055 471173 347916 213565 898693 206442 347104 619081 827992 617629 514894 511913 833189 497679 690485 536593 599690 487273 863289 797701 370033 155944 325228 915405 384234 884537 371242 265637 252635 738170 250701 159288 771005 665019 670035 814353 425082 135425 289871 538382 420086 672135 035048 360378 804789 019061 298528 245208 997877 464438 303394 964603 994865 259898 738418 217032 877702 130128 369932 275628 156716 409187 030908 125695 355416 715795 503060 809992 087109 389098 711611 369721 534808 772608 579127 435874 647108 923492 255965 143834 379611 475060 102760 252286 010168 672833 941770 118314 427846 483989 208445 124799 905993 948097 162186 128879 735008 739503 739554 132606 686744 852522 557769 224268 186065 387308 221746 852255 534703 410418 469083 302929 417131 246076 692579 907000 088155 755712 744773 715545 014455 778119 184500 672453 653424 693126 604017 571470 023172 271945 490977 619291 694598 555918 867300 874448 154684 190795 443370 611860 092560 598414 779596 520526 778111 390297 043283 854083 858487 477119 483904 / 1379 > 161423 [i]
- extracting embedded OOA [i] would yield OOA(161423, 713, S16, 2, 1378), but