Best Known (99, ∞, s)-Nets in Base 5
(99, ∞, 82)-Net over F5 — Constructive and digital
Digital (99, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(99, ∞, 160)-Net over F5 — Digital
Digital (99, m, 160)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 159)-sequence over F5, using
- t-expansion [i] based on digital (97, 159)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 97 and N(F) ≥ 160, using
- t-expansion [i] based on digital (97, 159)-sequence over F5, using
(99, ∞, 414)-Net in Base 5 — Upper bound on s
There is no (99, m, 415)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (99, 1655, 415)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51655, 415, S5, 4, 1556), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 113 925264 328848 247306 850889 186551 320474 503349 599171 826280 643623 205186 603087 663303 386041 332368 197420 053814 584124 254887 904923 246744 360986 679022 684136 009313 997463 771407 121154 094672 344575 435086 618487 370259 071577 243306 385404 647679 638665 525535 897457 075265 502537 630121 783617 354308 106706 347842 287557 719924 297294 387018 055535 535104 907054 935400 261877 152748 042330 015134 512764 568943 975320 918752 466045 465701 962850 205383 190959 958863 564221 784679 673133 627593 084777 475129 518132 502355 154461 093508 950657 903616 978529 359821 133189 454293 185413 748115 510665 094318 621257 408117 421032 556400 965717 767647 768650 367314 730865 540860 372097 046357 823760 462284 905073 476009 380658 477026 115940 054879 966463 217673 308649 584333 292330 223936 397880 204688 111195 645671 802594 750243 127268 975468 047723 206214 151919 233262 179840 332465 677849 308760 796677 319614 216936 879962 200462 448267 804288 918184 154992 645587 701777 736412 330760 881557 889540 003207 679561 838015 769487 311222 252767 586569 129891 611178 284364 677873 449703 851854 244941 218478 211302 571935 866470 427340 899654 709041 542273 616003 762721 713104 736737 115412 387612 970575 826604 095675 146781 457638 296000 142626 769496 302211 153271 575820 873748 492723 098735 268649 761565 029621 124267 578125 / 1557 > 51655 [i]
- extracting embedded OOA [i] would yield OOA(51655, 415, S5, 4, 1556), but