Best Known (15, 15+87, s)-Nets in Base 25
(15, 15+87, 126)-Net over F25 — Constructive and digital
Digital (15, 102, 126)-net over F25, using
- t-expansion [i] based on digital (10, 102, 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
(15, 15+87, 140)-Net over F25 — Digital
Digital (15, 102, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(15, 15+87, 1327)-Net over F25 — Upper bound on s (digital)
There is no digital (15, 102, 1328)-net over F25, because
- 1 times m-reduction [i] would yield digital (15, 101, 1328)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25101, 1328, F25, 86) (dual of [1328, 1227, 87]-code), but
- the Johnson bound shows that N ≤ 184120 860920 765395 596711 503302 174562 022270 048724 744249 014031 036610 630500 974067 722247 971010 574856 610965 363075 361962 808354 616425 181520 867720 627287 874641 406578 331177 922432 898075 815645 068589 127173 731543 180612 782719 900691 529034 320171 028896 773728 835663 662869 707159 920328 979948 631801 132486 721540 546867 662322 673577 973317 122688 201614 110867 141423 099255 269641 501628 814863 474677 514157 516739 753148 245232 548008 476178 402555 869697 072901 208768 254523 758478 039233 273009 065479 452960 824401 972062 088231 375192 859472 459130 053656 655880 267005 624278 471314 594317 081955 275575 017109 359276 683739 451717 083850 579078 964652 640335 897868 936982 788690 752201 510596 731362 509962 494769 140018 136173 968756 401925 086918 200303 149755 114256 899671 857415 288600 484834 242975 487736 649532 107922 855420 851860 119610 951001 880021 305608 113576 840662 375898 519083 012807 535083 826969 176146 452549 394657 537790 842796 325642 118814 076783 464024 674607 331728 202115 667535 904761 925456 579915 582048 002287 116670 319348 909646 394665 766805 109618 210594 259737 989273 777715 854314 075371 296813 481139 701507 156115 035208 187665 144674 689404 667638 602059 785925 791055 489324 448786 523744 833024 645132 493489 926032 283271 109659 890507 050333 417843 629529 965851 033538 586201 951379 213978 487891 585225 456162 075939 031357 122538 748146 199720 772214 585828 321974 931064 235314 406243 641408 298091 861153 004717 062289 121712 312676 340062 404044 440640 046530 967492 826500 263590 809017 182152 325841 872120 746395 648822 695124 821969 592043 017483 819731 478687 875094 584053 703023 588148 496789 383241 314366 537751 999359 005582 142026 546363 896759 641987 039636 232427 749501 906510 422049 279545 690660 624698 998149 389329 529253 856027 623311 484360 985170 400415 156710 037192 472807 454975 232566 007074 664458 586306 407471 949897 400499 845043 409353 220287 031820 206416 505202 853747 394187 687930 < 251227 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25101, 1328, F25, 86) (dual of [1328, 1227, 87]-code), but
(15, 15+87, 1328)-Net in Base 25 — Upper bound on s
There is no (15, 102, 1329)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 101, 1329)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1569 905016 659704 062539 311920 671763 567612 523559 912948 696552 360362 540669 656521 809764 372012 439952 061137 390340 546136 445951 748831 315281 501666 011465 > 25101 [i]