Best Known (112, ∞, s)-Nets in Base 5
(112, ∞, 95)-Net over F5 — Constructive and digital
Digital (112, m, 95)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (112, 94)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 94)-sequence over F25, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- base reduction for sequences [i] based on digital (9, 94)-sequence over F25, using
(112, ∞, 180)-Net over F5 — Digital
Digital (112, m, 180)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (112, 179)-sequence over F5, using
- t-expansion [i] based on digital (109, 179)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 109 and N(F) ≥ 180, using
- t-expansion [i] based on digital (109, 179)-sequence over F5, using
(112, ∞, 466)-Net in Base 5 — Upper bound on s
There is no (112, m, 467)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (112, 1863, 467)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51863, 467, S5, 4, 1751), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 333 841834 973489 191163 445781 706549 502377 927482 804615 265402 199619 755793 658774 087106 386879 920036 380344 877623 192996 920285 604125 867104 451411 788137 187547 671118 507990 988323 034089 853120 412534 179216 104432 554484 496152 665272 032965 258749 090693 936979 690646 567528 797631 770590 832285 778640 215353 614326 010619 386716 542236 987660 121928 603473 677243 940690 026482 570614 497604 493448 715106 024202 701354 024072 851852 006291 656509 094451 856849 999298 443897 447091 522337 711900 968785 319206 202900 000035 018550 458371 844040 167408 279355 445551 343886 245175 176412 852763 846427 849967 806208 064314 213556 487935 979050 525776 660936 905947 585602 393989 630150 756516 432664 394450 798616 992946 518247 922371 351852 064555 052689 099343 729532 388889 032100 802453 746298 867579 877170 337305 738264 082274 360215 755162 975090 163156 027910 327171 987987 855806 252043 014061 853557 616230 305375 136886 740863 997024 618980 751145 985858 213970 868381 894579 753837 155049 854188 064691 757255 217571 945378 089695 575327 014701 288168 782083 234750 388044 242761 237988 268622 869281 648703 076297 832407 065661 025345 834769 005474 005895 311289 517654 380102 763457 974926 915164 168735 097055 121117 965720 787494 690549 785953 509380 329502 971627 481754 151861 736286 079541 828673 987950 370797 040051 588278 000590 211689 971159 457135 638302 804205 232043 834320 756171 149555 860811 824894 440755 662389 066651 767315 779819 611520 906619 261950 254440 307617 187500 / 219 > 51863 [i]
- extracting embedded OOA [i] would yield OOA(51863, 467, S5, 4, 1751), but