Best Known (125, ∞, s)-Nets in Base 5
(125, ∞, 106)-Net over F5 — Constructive and digital
Digital (125, m, 106)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (125, 105)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 105)-sequence over F25, using
- s-reduction 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
- s-reduction based on digital (10, 125)-sequence over F25, using
- base reduction for sequences [i] based on digital (10, 105)-sequence over F25, using
(125, ∞, 200)-Net over F5 — Digital
Digital (125, m, 200)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (125, 199)-sequence over F5, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 121 and N(F) ≥ 200, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
(125, ∞, 519)-Net in Base 5 — Upper bound on s
There is no (125, m, 520)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (125, 2075, 520)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52075, 520, S5, 4, 1950), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 57 060319 686471 531032 126052 980711 420538 902855 307722 824728 015018 135958 372634 729699 820505 258014 252357 134608 719936 500262 350489 845866 748972 045577 515748 971278 700864 579537 204313 972957 815346 779961 587563 320180 178382 071505 798869 028987 428463 825560 453145 210761 267930 094519 675493 337978 220685 917252 302366 441267 200056 964867 547037 070099 037295 970864 051306 341775 361527 619123 351015 293127 123370 694703 837168 486284 795784 261824 498615 411161 183876 601598 865332 957280 520470 162469 540244 529678 040522 770782 277897 348207 307081 243004 307417 590906 261971 778592 327605 174300 084816 972928 736894 296836 015603 699615 024631 412452 418317 058184 359091 439541 453084 512297 299651 702361 469441 713984 324726 386376 046265 660061 090696 941815 797239 230806 209164 157922 350890 325076 084874 183043 036123 010508 711330 548938 436449 693790 679830 428811 247313 230016 395320 991174 868727 833949 821342 067921 746403 501020 355062 939990 253932 032812 703996 895252 923870 861288 917153 166126 369771 439691 707013 076841 487059 584178 426274 877206 074241 706100 108710 167611 693017 464659 201563 384839 439600 251373 681317 900481 078780 822279 223386 002406 222399 959843 103379 989101 715622 003321 740654 316522 614827 156624 995060 078512 009193 172944 231596 819785 126813 662307 720459 435587 787036 348831 598129 692845 547706 584853 397906 542585 840050 575779 979567 451852 946725 467351 526501 246294 669019 762304 044143 699965 366737 396689 452165 715215 560606 381064 899626 469293 290050 768541 941636 070864 229460 348186 644034 078283 104335 564341 743760 505972 705407 133778 975070 637073 940815 753303 468227 386474 609375 / 1951 > 52075 [i]
- extracting embedded OOA [i] would yield OOA(52075, 520, S5, 4, 1950), but