Best Known (16, 16+94, s)-Nets in Base 25
(16, 16+94, 126)-Net over F25 — Constructive and digital
Digital (16, 110, 126)-net over F25, using
- t-expansion [i] based on digital (10, 110, 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+94, 150)-Net over F25 — Digital
Digital (16, 110, 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+94, 1405)-Net over F25 — Upper bound on s (digital)
There is no digital (16, 110, 1406)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(25110, 1406, F25, 94) (dual of [1406, 1296, 95]-code), but
- the Johnson bound shows that N ≤ 521410 139583 097071 703776 399127 676639 128748 155143 382235 339573 705511 685566 571544 095505 708144 085870 190084 794654 577966 250045 380287 263489 552181 122548 984472 182463 727845 517576 506259 477950 599018 770117 392976 666001 713360 041734 831017 190214 536997 789723 191048 510436 241470 094655 953235 642049 600913 471133 570676 011151 320498 214440 032717 244260 737216 091123 655924 145314 340278 466126 050001 906314 754718 848628 117066 326597 574300 502221 862885 555533 655412 134022 643713 169138 387528 993087 419217 221080 452422 024534 072839 408141 719083 244190 376497 366490 940781 144146 107869 025338 149312 858807 499173 760463 113755 429073 218510 490563 118141 683275 968203 056823 747976 286923 316658 607741 024728 065195 837435 434854 702991 647119 950865 537502 898254 435530 943343 695578 520597 603978 772431 814070 846668 339161 721530 139455 517932 970497 275067 123105 756497 612814 296131 350197 106223 531302 914434 956428 232834 763811 091094 979294 993436 112916 514476 062452 578994 884391 713915 692041 992632 230675 504521 408233 538927 936456 560601 445557 994545 273537 756974 700900 954250 500795 460467 970493 818229 530044 627280 844152 075065 992564 513452 438343 901489 024067 618135 429166 002123 930968 396268 828169 907901 209375 370621 416880 842040 623043 641224 419756 414299 853110 395360 679062 989411 105750 328901 559702 744938 264252 700854 222608 688534 495521 185271 980740 612323 680675 318753 292064 376692 032566 038232 312671 799761 203233 643302 576833 178371 259920 611100 452588 968566 271618 800956 426419 172990 811392 660665 061772 742697 449834 419225 303003 328665 114862 532688 902631 789262 541804 063360 097167 369099 506916 828531 813568 629456 519572 239206 296088 769273 513118 251585 804605 024552 852141 886836 783517 463988 761318 803598 986296 878693 236977 286310 247969 074501 827526 235510 122818 541295 072349 372369 003587 802931 959174 489452 313463 012386 427549 479441 350627 225296 432567 214637 460389 043534 932494 178807 488150 340400 872157 889949 754556 584089 108048 553052 943874 280809 099153 635812 398904 < 251296 [i]
(16, 16+94, 1406)-Net in Base 25 — Upper bound on s
There is no (16, 110, 1407)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 6089 910828 884820 635536 648756 889951 758796 645085 618675 353361 834856 349391 964576 930088 520871 102185 377019 534551 025714 993663 036012 398352 272894 906127 307817 289625 > 25110 [i]