Best Known (87, 87+∞, s)-Nets in Base 5
(87, 87+∞, 82)-Net over F5 — Constructive and digital
Digital (87, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (87, 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
(87, 87+∞, 150)-Net over F5 — Digital
Digital (87, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (87, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(87, 87+∞, 366)-Net in Base 5 — Upper bound on s
There is no (87, m, 367)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (87, 1463, 367)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51463, 367, S5, 4, 1376), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 738631 284541 016078 865920 137291 878719 250614 238633 784661 285555 882961 076946 104007 970538 638861 952010 418013 265611 528038 646076 987942 733201 913820 262643 359604 317919 261150 894026 215768 725371 871747 656807 818290 238542 705209 544196 735637 317467 481145 442484 747017 790023 331459 610344 629875 269915 619951 915080 770818 098828 253756 732733 174223 102174 034752 643859 316416 944919 091073 191817 236816 088742 114659 458762 649343 486873 600852 613244 422677 318361 313375 848276 835522 015657 954955 590220 070313 194060 281411 470158 392987 529890 425614 547276 568277 301483 542421 810490 253578 035384 976098 810126 032392 064896 225925 560675 372221 423112 358484 093188 471490 419552 856114 782761 128389 424083 110093 852136 055044 803303 283529 988813 522784 140486 318518 145822 444976 976265 318357 021733 073449 693568 238045 756672 509149 849534 930210 220010 379037 874363 596021 045005 740596 950907 971756 049399 969730 413271 824642 029594 824585 605831 230172 401626 171444 522451 265871 189734 409477 324607 072195 597458 394182 547833 151602 602325 011037 413282 145760 710415 008111 912866 385339 121130 283734 917298 943400 965072 214603 424072 265625 / 1377 > 51463 [i]
- extracting embedded OOA [i] would yield OOA(51463, 367, S5, 4, 1376), but