Best Known (19, ∞, s)-Nets in Base 25
(19, ∞, 148)-Net over F25 — Constructive and digital
Digital (19, m, 148)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(19, ∞, 162)-Net over F25 — Digital
Digital (19, m, 162)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 161)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 162, using
(19, ∞, 506)-Net in Base 25 — Upper bound on s
There is no (19, m, 507)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (19, 1011, 507)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251011, 507, S25, 2, 992), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 986375 728297 991256 928132 262234 679303 296345 300146 355531 908430 882456 704903 928751 235377 252318 055605 708004 508719 780276 103568 600903 422044 386805 156308 565532 789828 544430 149816 844755 712190 111544 181579 668003 992504 462448 338401 256232 537325 888003 305772 464748 107412 395254 950415 790077 839683 374625 415957 169271 500736 500443 775150 640480 601652 736327 436860 695039 932586 721531 864819 896674 656496 670673 833336 087071 245073 377793 665180 324088 156882 589774 550408 522787 199761 038277 405473 978051 226328 716862 733761 709623 868572 478374 844333 885214 825991 701153 217778 786326 537104 467567 163172 839360 184609 960682 449931 223521 722392 409503 915531 366944 394273 734183 172556 536496 893303 136539 221722 864329 906117 121041 474708 674152 764637 589047 880861 513900 037301 398224 215701 193846 301027 540062 414415 419966 436132 224931 200705 971066 564981 868401 174114 534424 755836 134842 835727 856160 664864 779203 620261 243471 645031 803657 549001 897060 418245 441273 648515 411774 217679 358016 868701 258528 718459 506088 046501 154139 665533 330456 080309 873001 593351 897875 617001 775700 798121 467030 542222 132784 232407 761572 508146 767887 729253 846955 173697 670122 096046 028762 177431 549243 041910 535703 143742 492864 627365 015880 794135 950667 585767 199294 379809 641278 811467 408559 142886 423052 699730 039326 939342 514857 107925 927974 932865 707311 383038 774109 001338 005103 167376 478688 080502 066313 667419 737108 245569 371836 687449 423443 450270 829101 580436 496487 831010 985155 222799 494256 756797 666454 809891 956045 930783 147923 648357 391357 421875 / 331 > 251011 [i]
- extracting embedded OOA [i] would yield OOA(251011, 507, S25, 2, 992), but