Best Known (13, 13+82, s)-Nets in Base 25
(13, 13+82, 126)-Net over F25 — Constructive and digital
Digital (13, 95, 126)-net over F25, using
- t-expansion [i] based on digital (10, 95, 126)-net over F25, using
- net from sequence [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
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(13, 13+82, 1143)-Net over F25 — Upper bound on s (digital)
There is no digital (13, 95, 1144)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(2595, 1144, F25, 82) (dual of [1144, 1049, 83]-code), but
- the Johnson bound shows that N ≤ 265 689220 527717 804463 629396 568234 966830 016683 163224 153068 023564 264417 250218 574032 427178 876693 008345 899923 744300 764710 173836 713459 134257 867373 245167 176491 922834 072127 150801 234377 203821 952473 060767 997973 187830 581109 013474 641895 044790 579344 606868 650055 824741 707169 122283 072693 462072 573531 958683 871889 547576 514816 698913 929845 493195 322835 488045 876209 113575 206133 341840 226015 658288 140924 415088 865455 529973 856285 710615 313095 355403 023628 953772 750696 477790 372320 800534 795906 951025 673990 483075 034491 880129 811174 484553 481599 988045 756796 026642 911068 919792 709889 200209 457124 809356 405697 363365 663637 966504 607961 305975 889236 854649 965406 309094 922579 725284 543617 806483 750454 037377 411374 631532 556813 982234 834464 169020 625522 236742 099758 268614 682225 667706 605827 067261 857201 077598 150104 067437 903862 001368 363092 478306 758137 019078 755044 079085 798513 751154 390763 595824 953867 589745 722598 375746 161099 484027 810318 722177 384337 299812 389714 335234 801802 627698 419755 843246 646351 017314 664345 168606 035005 642911 699686 560965 668584 462596 575994 852275 729661 222019 896077 335271 925038 861884 304913 975663 277077 686018 251275 701854 973641 355205 913002 729968 226107 590750 956935 510381 899582 295369 044412 976208 291306 426323 743078 365796 351536 291420 562389 878013 723786 285278 886166 490083 278657 932199 253476 326592 825902 789068 259498 878204 561650 934099 432081 080238 756840 392397 703190 670454 919015 728591 128941 634357 153691 447989 811999 118664 480363 150183 368671 523126 825818 293174 849471 622999 032175 133986 370644 687869 876210 600094 096234 507828 < 251049 [i]
(13, 13+82, 1144)-Net in Base 25 — Upper bound on s
There is no (13, 95, 1145)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 6 431472 416563 066348 579397 982717 436612 833926 893173 285445 848095 848186 689695 886865 806020 885357 583845 163520 135919 662402 706385 279232 811545 > 2595 [i]