Best Known (16, 105, s)-Nets in Base 25
(16, 105, 126)-Net over F25 — Constructive and digital
Digital (16, 105, 126)-net over F25, using
- t-expansion [i] based on digital (10, 105, 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
(16, 105, 150)-Net over F25 — Digital
Digital (16, 105, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(16, 105, 1424)-Net over F25 — Upper bound on s (digital)
There is no digital (16, 105, 1425)-net over F25, because
- 1 times m-reduction [i] would yield digital (16, 104, 1425)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25104, 1425, F25, 88) (dual of [1425, 1321, 89]-code), but
- the Johnson bound shows that N ≤ 47117 292527 400637 258642 313389 723232 611206 154368 552547 673050 782005 763349 846450 814830 339959 626338 449235 511319 557170 911424 197444 182517 266115 934036 716073 051676 629576 909274 698439 272763 909088 309717 411902 369777 847316 349317 746159 241101 463130 472615 382400 421967 312260 220259 307065 029759 621887 899042 005846 004415 549652 468588 673622 765828 837947 068380 993970 673669 105333 848494 119491 130718 510675 417978 564335 555162 032920 416261 043432 776542 209794 275599 647244 993341 941495 441414 585708 594614 741994 232638 419596 556057 038290 200635 456808 123377 725518 398143 835510 041230 536307 423587 143172 161258 200687 023079 992359 922425 989272 767687 586178 666812 379015 637674 974296 391145 930624 588663 701049 632960 583870 370655 684401 819443 683826 099991 263545 740904 097199 288508 376705 756756 407206 346291 534301 662673 573621 553738 278366 677124 608705 653528 462965 004076 634966 263820 280063 264316 549223 128038 363101 643765 017364 870393 373331 298612 093870 526307 151350 325659 856435 775900 733031 645087 999368 932469 701764 653017 874323 998540 781931 463618 162044 733384 099681 602268 416844 436857 354751 299348 037461 346786 036694 143258 454745 721263 624886 324956 261263 374146 529912 393207 709306 502348 442825 163392 422489 620738 682832 721597 824324 062311 803382 405089 589955 804352 295014 228221 414893 746215 700867 339582 991201 356423 366798 929337 341323 896475 550193 339727 698599 378795 464019 288571 076101 260433 937712 130066 388470 231163 671290 196302 020724 424568 262831 267964 637553 359656 225065 367040 844627 277290 949695 741931 847522 006082 133302 280712 758865 167216 921237 095014 224064 219356 423880 964364 175499 135266 722631 074832 848094 492279 147365 474885 137446 422793 937572 128961 769386 632889 624326 498229 865962 693666 355084 650384 516590 908361 399932 434571 500759 971447 457998 880527 868546 023095 321710 259564 889738 622269 371537 374388 544514 143423 296185 629553 305292 291760 105185 145617 611203 764381 170986 256482 122424 136155 855800 856554 122271 004118 424167 524163 410856 279326 556925 405043 705815 934235 < 251321 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25104, 1425, F25, 88) (dual of [1425, 1321, 89]-code), but
(16, 105, 1425)-Net in Base 25 — Upper bound on s
There is no (16, 105, 1426)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 104, 1426)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 24 831126 908249 105702 340010 539695 260863 899417 838214 239176 536185 795317 166028 515349 851190 427066 662105 621323 671815 816682 993904 652186 982256 105486 757825 > 25104 [i]