Best Known (16, 16+93, s)-Nets in Base 25
(16, 16+93, 126)-Net over F25 — Constructive and digital
Digital (16, 109, 126)-net over F25, using
- t-expansion [i] based on digital (10, 109, 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+93, 150)-Net over F25 — Digital
Digital (16, 109, 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+93, 1410)-Net over F25 — Upper bound on s (digital)
There is no digital (16, 109, 1411)-net over F25, because
- 1 times m-reduction [i] would yield digital (16, 108, 1411)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25108, 1411, F25, 92) (dual of [1411, 1303, 93]-code), but
- the Johnson bound shows that N ≤ 3195 500974 872566 162983 480635 330463 469970 984753 584864 534162 135102 096130 761016 904990 098166 941067 355059 688821 496727 759118 822974 701613 274285 858607 176648 617476 465541 126678 862969 218057 036801 665482 548153 945066 637762 711741 158821 708838 240424 089338 206588 132486 511191 313679 947025 481512 200259 094609 674000 540319 386743 985604 428469 745373 049844 338377 013357 112446 741465 890870 415329 160130 815112 418494 159658 643955 757408 877062 665515 748253 649349 334441 349816 450947 857847 449917 775281 498261 368795 244736 535829 288870 609289 867766 200372 681629 104325 258987 538217 310582 805303 536535 145104 072701 436272 821624 235090 953328 735173 284933 543753 579724 154292 735232 081819 133097 871050 378552 441312 943180 052106 782624 044771 712088 222545 679377 243815 652067 661274 481702 937621 077168 740990 449817 420716 713756 652144 650938 545773 190611 779803 024301 369223 128145 569263 552409 812382 583685 182128 592098 803297 278456 317069 978136 334317 014040 799334 081093 763042 665859 283309 498661 011158 345782 652456 905863 264257 488302 792693 606413 296466 289288 457821 452488 066787 926393 871084 829738 906884 569335 973786 079691 491897 363492 844726 487770 399793 992544 443537 038057 204922 039366 343544 487264 158929 162140 656853 879911 179915 407329 669994 958440 176574 439545 921551 370336 999471 775588 041737 157565 844209 766400 430180 805730 976867 443023 117508 522148 651085 957957 576019 758377 720959 656166 843520 740332 422719 295055 406153 759871 698292 690246 730286 091216 128775 958675 286844 487749 668095 790610 435760 130272 344480 773357 670785 018597 134169 406687 467832 329813 538920 295744 387872 652035 619573 810226 161367 141277 170303 251136 494959 537747 539555 061319 347743 015912 255150 866242 949632 307241 151904 611725 585228 616847 397293 936462 377895 819725 938218 673330 892811 739742 118729 589202 476611 468436 191006 873924 662941 280804 546927 446704 623842 529181 765966 451617 399743 890384 346049 558571 999849 883351 196983 680616 362667 031572 570232 724907 582256 845824 499110 163865 627312 634401 < 251303 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25108, 1411, F25, 92) (dual of [1411, 1303, 93]-code), but
(16, 16+93, 1411)-Net in Base 25 — Upper bound on s
There is no (16, 109, 1412)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 108, 1412)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 9 610895 791068 955750 225167 326354 150320 984974 353507 647344 303523 222875 620321 661735 754916 540857 683312 754174 882578 174921 326721 660281 934499 110847 123530 719425 > 25108 [i]