Best Known (126, 126+∞, s)-Nets in Base 5
(126, 126+∞, 107)-Net over F5 — Constructive and digital
Digital (126, m, 107)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (126, 106)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 106)-sequence over F25, using
- s-reduction 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
- s-reduction based on digital (10, 125)-sequence over F25, using
- base reduction for sequences [i] based on digital (10, 106)-sequence over F25, using
(126, 126+∞, 200)-Net over F5 — Digital
Digital (126, m, 200)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (126, 199)-sequence over F5, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 121 and N(F) ≥ 200, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
(126, 126+∞, 523)-Net in Base 5 — Upper bound on s
There is no (126, m, 524)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (126, 2091, 524)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52091, 524, S5, 4, 1965), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 344562 249249 843455 593266 369208 355797 078760 400947 813618 305771 792504 425986 173452 005302 290091 318560 424881 244643 799927 004595 204957 622796 598571 668340 508326 008841 328058 936985 070221 434434 264104 211095 371465 048452 164362 722784 685897 024083 167155 389320 101360 909256 978151 374538 492370 180229 239896 930327 601883 396468 983759 187368 730121 793561 871400 596748 942802 818929 443952 300008 377661 625863 296537 101909 172323 930392 398308 848728 374614 310961 642978 527874 336766 187434 689340 295176 002835 507174 135268 463023 991442 502678 477592 719163 110892 200418 192333 585155 287633 451504 113496 228771 137682 518499 852592 363788 014074 999051 893868 968214 735726 015930 753623 094042 836347 879106 033280 229112 233613 874162 652537 055553 750588 311680 677012 166853 948113 588481 836891 187560 394968 862798 635647 136556 805107 900847 795079 178601 849771 018931 492603 664095 879701 615944 532910 158059 936146 336214 212668 687516 197798 786424 182037 889233 901862 704250 791218 570759 114593 571621 224945 947398 863506 848053 199626 906050 832627 390955 977440 027364 530127 966732 545724 216896 182298 861904 340675 215067 398046 266639 436079 227386 271958 580227 565597 764305 301953 902969 710169 465018 105919 141938 891998 097978 022224 338807 605386 514437 716547 471271 237333 665929 769062 137302 584611 189019 724260 688637 943910 167742 770730 591588 644075 537773 104768 287686 801620 892471 408369 209443 026853 341429 275016 844958 415016 342220 092668 088190 799635 462969 458351 657025 127936 425899 654967 480184 136901 886626 401137 820703 027711 320575 396597 585423 190043 565181 369159 509949 806619 033552 124164 998531 341552 734375 / 983 > 52091 [i]
- extracting embedded OOA [i] would yield OOA(52091, 524, S5, 4, 1965), but