Best Known (15, 15+93, s)-Nets in Base 25
(15, 15+93, 126)-Net over F25 — Constructive and digital
Digital (15, 108, 126)-net over F25, using
- t-expansion [i] based on digital (10, 108, 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
(15, 15+93, 140)-Net over F25 — Digital
Digital (15, 108, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(15, 15+93, 1313)-Net over F25 — Upper bound on s (digital)
There is no digital (15, 108, 1314)-net over F25, because
- 1 times m-reduction [i] would yield digital (15, 107, 1314)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25107, 1314, F25, 92) (dual of [1314, 1207, 93]-code), but
- the Johnson bound shows that N ≤ 20 290419 551137 578268 374851 704200 880048 453153 777021 106059 740431 911553 688490 063185 293476 689021 143151 816286 092914 885254 104265 760764 210559 800256 506415 829314 845467 731390 162305 606371 929104 498928 402653 071725 848939 606223 869690 187749 057013 486425 666755 303150 159847 377048 215639 981709 984185 411762 306639 458112 932701 009068 260034 041339 947449 375401 204173 564421 732922 551473 288116 419087 351921 199175 915991 695593 410093 711678 926776 226678 340305 775958 519408 414760 518531 125885 959975 097854 880951 039367 687219 284490 358044 450886 317037 370525 035430 628265 984770 820397 741152 767334 473671 370414 714949 622135 090128 495191 983556 341797 150740 500578 379683 214445 273223 252496 179556 015193 444292 133981 105583 987888 879368 430076 931247 798558 207860 848639 590787 923740 330258 409526 536904 512589 597922 486954 687332 361241 750376 890993 510870 596865 812269 879494 973939 562036 906857 232829 561398 581207 414012 393266 141407 131114 425712 964150 844295 646286 441681 846505 654352 751479 199013 345013 683569 017668 147577 880007 362662 806497 622287 597756 054595 728672 392702 871967 401360 230386 007642 734311 213775 573247 839271 119916 496438 589114 665424 894318 916334 045054 040547 890642 746272 732507 441226 032070 233089 335399 018627 688451 805443 741899 778197 032684 731552 733975 087716 339799 610736 537853 821277 669402 240645 623488 460295 989363 111135 773046 571033 255041 863396 627003 944909 973052 454051 859058 004777 808999 454522 047733 443739 475863 047577 618524 642539 164550 243758 923798 862907 642552 385157 142105 169633 726938 393782 386580 577301 421423 800302 362104 974234 307595 404088 983339 027315 041820 277603 324824 124622 797768 163483 174281 899141 314466 981425 895900 551695 906153 225497 476100 188753 023708 801042 484625 114469 310090 263459 507502 601938 444980 741279 886263 692621 642002 834876 751895 221187 658456 834626 036563 435578 241991 < 251207 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25107, 1314, F25, 92) (dual of [1314, 1207, 93]-code), but
(15, 15+93, 1314)-Net in Base 25 — Upper bound on s
There is no (15, 108, 1315)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 107, 1315)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 385295 281184 524049 567346 017335 004401 411883 388264 868072 916207 043555 265083 579768 136984 009135 886258 961099 984992 484286 969193 774292 603014 609781 834530 254705 > 25107 [i]