Best Known (31, 31+89, s)-Nets in Base 5
(31, 31+89, 72)-Net over F5 — Constructive and digital
Digital (31, 120, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
(31, 31+89, 295)-Net in Base 5 — Upper bound on s
There is no (31, 120, 296)-net in base 5, because
- 2 times m-reduction [i] would yield (31, 118, 296)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5118, 296, S5, 87), but
- 4 times code embedding in larger space [i] would yield OA(5122, 300, S5, 87), but
- the linear programming bound shows that M ≥ 92 743399 900862 116398 314369 052090 550126 284355 781257 772549 495829 610512 418537 871494 625567 999901 606760 627959 649237 296008 120980 299691 603506 922909 788893 616486 837985 916789 737214 178266 621628 613730 286070 935810 651796 405891 302564 997875 456930 830647 156343 496128 880620 967738 901987 090841 816621 433333 167150 135903 629871 184839 128187 638441 235596 630165 375130 891213 826158 009639 024441 772247 462113 289821 184079 138772 562344 820169 350642 944923 305482 412716 167326 819941 353204 107737 868834 533201 747860 609032 159118 214622 139930 725097 656250 / 3 710278 980401 980551 220483 820828 987938 920959 186590 831261 723474 350289 521560 732813 048064 057102 028339 481698 668204 691387 747409 050856 574877 247032 433188 825187 983571 279404 160492 157548 682327 835041 171048 208603 700692 507634 167243 751266 617772 087116 978173 860301 384710 485853 996094 566932 302808 581307 058940 891026 669036 037112 035772 994002 366156 831484 390120 294580 328410 249804 762812 879292 433580 846402 913816 877042 123156 256859 569754 162628 179267 > 5122 [i]
- 4 times code embedding in larger space [i] would yield OA(5122, 300, S5, 87), but
- extracting embedded orthogonal array [i] would yield OA(5118, 296, S5, 87), but