Best Known (55, 55+∞, s)-Nets in Base 5
(55, 55+∞, 82)-Net over F5 — Constructive and digital
Digital (55, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (55, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(55, 55+∞, 108)-Net over F5 — Digital
Digital (55, m, 108)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (55, 107)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 55 and N(F) ≥ 108, using
(55, 55+∞, 237)-Net in Base 5 — Upper bound on s
There is no (55, m, 238)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (55, 947, 238)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5947, 238, S5, 4, 892), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 106337 055818 597293 166798 378000 258904 488362 820660 507907 491521 053883 326637 164020 865323 343745 409387 573507 188577 547553 767267 655704 468511 591257 154564 068604 578514 385068 255450 194334 350908 782598 212213 100709 387052 430963 551922 987605 716819 739049 538898 784857 115410 167005 085569 631844 287594 701073 935686 941334 068755 705212 513620 519118 377242 555746 893289 846282 369043 243237 772428 599188 498753 533035 369340 295391 808030 888122 560825 727088 273289 151827 476679 804191 286992 131047 185301 976646 617720 479420 887393 856991 886601 468044 031779 132968 953582 825139 301820 724375 938220 873261 777588 610383 297000 695326 905219 170305 150876 413589 945231 856208 786699 497847 856002 614996 828725 679733 906872 570514 678955 078125 / 893 > 5947 [i]
- extracting embedded OOA [i] would yield OOA(5947, 238, S5, 4, 892), but