Best Known (89, 89+∞, s)-Nets in Base 5
(89, 89+∞, 82)-Net over F5 — Constructive and digital
Digital (89, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (89, 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
(89, 89+∞, 150)-Net over F5 — Digital
Digital (89, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (89, 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
(89, 89+∞, 374)-Net in Base 5 — Upper bound on s
There is no (89, m, 375)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (89, 1495, 375)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51495, 375, S5, 4, 1406), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5702 121929 793411 718735 803454 830573 090256 193014 732764 738677 000706 598808 540745 307056 350002 187830 464070 300838 507437 976667 589775 588099 713777 397768 548501 451639 329315 715427 008771 901467 995622 300114 345369 107061 394176 023040 467806 186677 917380 042798 453607 037154 129863 959453 839345 166223 727207 042273 468500 518432 322536 280911 779375 641101 051948 534784 399733 369663 259314 891228 657030 681492 338614 905921 612081 141140 638049 406383 346709 085860 304713 040525 723888 556808 754775 159859 959954 412519 255854 137133 750071 670116 247950 278529 475583 545584 814791 150523 962394 784870 614429 379444 410879 256838 158687 090923 892433 391827 709815 405109 630392 225911 546022 645299 410665 405183 604938 290064 440926 559176 352223 463452 943012 030491 412084 582288 161919 531426 822632 930868 786625 115216 689277 917061 706572 823640 968623 175687 268856 817390 488686 859621 636577 813867 794314 556610 300923 056696 634127 005832 155723 821426 691369 567973 252143 177583 428800 954535 129288 899802 178175 609158 765756 395311 889282 524398 633423 401948 219470 299869 417324 933274 581035 764017 209392 563735 258906 644953 920406 226899 331159 074790 775775 909423 828125 / 469 > 51495 [i]
- extracting embedded OOA [i] would yield OOA(51495, 375, S5, 4, 1406), but