Best Known (14, 103, s)-Nets in Base 25
(14, 103, 126)-Net over F25 — Constructive and digital
Digital (14, 103, 126)-net over F25, using
- t-expansion [i] based on digital (10, 103, 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
(14, 103, 130)-Net over F25 — Digital
Digital (14, 103, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(14, 103, 1226)-Net over F25 — Upper bound on s (digital)
There is no digital (14, 103, 1227)-net over F25, because
- 1 times m-reduction [i] would yield digital (14, 102, 1227)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25102, 1227, F25, 88) (dual of [1227, 1125, 89]-code), but
- the Johnson bound shows that N ≤ 4 790276 955301 037203 318884 230398 321367 371919 473957 943036 606147 412321 862989 618843 698564 674901 086319 215538 024817 390838 488402 888346 083671 515055 828798 538972 117379 403675 717352 723362 216417 228944 773346 064450 366349 081691 821613 528332 401607 511060 919482 812831 975885 949581 859228 646158 011291 199819 543084 751393 684577 210200 218903 426775 152334 353118 206011 575155 347082 189005 398596 913123 001716 826328 025640 915293 628005 224842 252479 676014 572761 582467 415696 955649 934158 911191 720042 913335 234945 099568 225204 315523 991945 389459 358568 670429 685259 352182 083669 089539 305789 857659 671303 661904 606564 236279 880089 411917 795516 912086 813254 630506 983879 137623 509527 705363 443469 772567 329337 127031 247755 399636 740321 442492 656009 910357 270766 575302 711932 700059 923863 845805 169620 002184 215277 841488 300429 518719 338986 829994 914700 900384 290419 495910 715991 570240 675074 171781 585430 009022 349601 463150 825197 294521 966191 330569 480757 359012 880239 964090 999357 917521 624596 066401 770514 448570 286794 627162 105919 592532 175264 371987 354897 247739 720809 557323 121455 354078 465782 933356 799668 436480 569239 916838 659284 802872 361603 243946 127158 695595 298781 701854 544933 185570 913878 157112 097151 620246 188852 579560 943577 838143 920442 161353 880750 126116 312066 064990 135101 435236 943484 856166 058916 767286 541666 212890 046948 928021 504498 435085 235300 418114 314752 929204 877661 905057 790704 063860 610048 277571 337306 294052 425756 421067 533473 597918 707869 155032 887242 589615 302622 753302 647787 313998 538234 454138 873989 048273 810788 739459 897484 695959 668113 871961 706814 099451 186756 122962 074190 612627 838175 589537 130954 292861 559827 215749 609581 608740 334516 359242 652885 518491 367160 < 251125 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25102, 1227, F25, 88) (dual of [1227, 1125, 89]-code), but
(14, 103, 1228)-Net in Base 25 — Upper bound on s
There is no (14, 103, 1229)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 102, 1229)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 40077 057342 023895 205621 628648 894985 828262 566471 817591 398109 079217 823795 765749 060867 836345 097610 492856 208100 157512 737942 542263 220230 733873 435425 > 25102 [i]