Best Known (14, ∞, s)-Nets in Base 25
(14, ∞, 126)-Net over F25 — Constructive and digital
Digital (14, m, 126)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 125)-sequence over F25, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
(14, ∞, 130)-Net over F25 — Digital
Digital (14, m, 130)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(14, ∞, 385)-Net in Base 25 — Upper bound on s
There is no (14, m, 386)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (14, 769, 386)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25769, 386, S25, 2, 755), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 259 302484 200516 651923 671973 001117 889464 521477 508822 715148 062375 492318 485191 631546 347252 978549 952971 220629 411047 319839 216914 969624 654703 575186 820148 767385 004671 983343 860518 830363 980469 987842 040853 552455 764391 926233 677977 788223 775741 245972 242432 209766 508543 178108 713588 934107 234636 350871 072340 874817 760892 996416 795512 033836 578300 385316 852031 490710 181029 266606 340435 404558 426790 340759 981158 095849 452276 952724 030102 630688 829991 097032 949432 494061 000160 179894 917744 350665 055019 550760 960104 147221 329546 950006 691785 508591 456836 763905 992592 971636 923467 912285 760161 433101 446104 369230 119683 988588 245020 555637 421711 809379 828356 333987 331284 579576 440816 631023 355554 432745 355016 934966 122017 250676 954612 780822 943110 230490 984696 777144 053459 101779 330434 415763 270707 103567 518453 163560 810428 717440 594877 501081 174913 352418 470563 614237 576117 514285 971725 576284 013901 559839 118425 296327 279836 222150 307949 093736 857743 756436 419888 614598 620086 162341 608054 817897 874883 028723 535038 366202 089370 059787 806032 353001 556175 175380 088099 093197 975908 252687 956117 327975 824799 791981 778440 685957 320965 826511 383056 640625 / 21 > 25769 [i]
- extracting embedded OOA [i] would yield OOA(25769, 386, S25, 2, 755), but