Best Known (16, 16+91, s)-Nets in Base 25
(16, 16+91, 126)-Net over F25 — Constructive and digital
Digital (16, 107, 126)-net over F25, using
- t-expansion [i] based on digital (10, 107, 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, 16+91, 150)-Net over F25 — Digital
Digital (16, 107, 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, 16+91, 1416)-Net over F25 — Upper bound on s (digital)
There is no digital (16, 107, 1417)-net over F25, because
- 1 times m-reduction [i] would yield digital (16, 106, 1417)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25106, 1417, F25, 90) (dual of [1417, 1311, 91]-code), but
- the Johnson bound shows that N ≤ 494 010306 855883 715569 097268 888316 232852 985842 869907 699498 456406 145108 679700 213879 182837 759294 529423 995868 242207 260725 350786 816017 821533 008179 926695 497040 388609 377554 244338 863499 401754 941888 787017 561033 640380 672257 919667 201905 984179 648372 755285 874988 088098 122665 656058 045590 510800 356529 011601 549445 608151 032964 724983 906667 526315 370769 896970 464846 874453 826783 672054 959333 151171 448182 656359 332354 582931 373999 795649 114633 423999 853404 375617 603059 885452 419702 820102 447339 474060 827020 205645 808804 958699 959934 415693 099028 415036 664689 858019 490455 596307 683251 578155 790722 819065 721027 877398 179756 232230 461125 249690 503897 139694 736553 840764 386408 128807 626999 788892 846395 583780 534378 721162 832177 908974 391020 670322 139818 422240 703233 284723 919299 434745 026332 633667 768658 402471 332022 023325 816851 887894 491038 309268 709818 746203 839039 877430 992949 003461 364352 941512 439074 845283 354539 283493 506032 457794 866190 435083 435492 493682 335435 235492 049741 507823 339018 393501 750140 355460 051822 698156 323312 399506 800976 164299 436249 869408 334826 847091 376711 851260 650746 068159 331710 041986 116088 610631 521162 455708 950391 404352 155554 841982 250565 376732 950929 337778 368100 228528 080511 048421 722099 276406 932244 711782 143163 715948 082697 660537 078298 289587 536421 287271 355343 120144 570957 155057 389939 513123 017830 085704 174293 431457 607505 796073 275024 771209 790381 789634 522756 705179 838146 195585 815935 782341 999514 476186 898339 613626 629012 131454 475071 906976 505940 792569 354875 316379 955521 471263 366964 361705 553192 174466 271985 286404 202119 250013 377170 130826 699281 258662 421764 713503 464379 362065 562690 905684 406740 629674 787535 447777 486970 493028 383869 452913 154960 354837 244219 698440 061486 366201 242588 034376 606791 483985 190924 889371 987178 913072 119750 477543 970194 533005 852733 390692 220695 518442 294299 282754 389430 399245 184910 342302 200258 661092 511314 919741 390645 673405 171318 436871 362564 049692 025357 098850 822626 < 251311 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25106, 1417, F25, 90) (dual of [1417, 1311, 91]-code), but
(16, 16+91, 1417)-Net in Base 25 — Upper bound on s
There is no (16, 107, 1418)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 106, 1418)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 15214 022283 940777 113707 245949 378562 011757 317049 834657 793188 342330 439862 799935 325502 106509 778641 121339 502706 109258 502670 557083 915981 006378 651935 887025 > 25106 [i]