Best Known (72, ∞, s)-Nets in Base 5
(72, ∞, 82)-Net over F5 — Constructive and digital
Digital (72, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (72, 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
(72, ∞, 132)-Net over F5 — Digital
Digital (72, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (72, 131)-sequence over F5, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
(72, ∞, 305)-Net in Base 5 — Upper bound on s
There is no (72, m, 306)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (72, 1219, 306)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51219, 306, S5, 4, 1147), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 326 781379 334290 206731 532621 326810 656293 117062 744591 367626 085403 688826 408725 584438 737148 713424 959825 282065 160204 943766 590498 031625 421529 842644 401772 550286 097352 630125 316327 127456 306131 119672 940275 930825 286202 377935 021724 489096 726629 564551 753764 011029 982660 902066 690256 293868 021226 906099 050879 419800 606195 472188 091440 280503 254687 078773 876885 970413 683381 238519 719045 767898 644581 190362 635044 531452 900860 292545 646456 101504 025179 481616 138994 699115 559400 434601 974183 564233 331888 092747 723914 688434 128095 762748 027768 811872 802010 057680 675235 043276 616239 287745 840369 679964 129825 600911 500963 437724 811664 557914 559437 046583 332275 529028 634626 260925 563065 937297 849505 509353 477510 806228 279718 550948 481956 020461 892159 781867 900815 167291 673767 693328 835445 815777 407649 853686 323909 742795 869961 841671 526340 545349 486134 868338 629343 726266 067438 057660 865524 667315 185070 037841 796875 / 287 > 51219 [i]
- extracting embedded OOA [i] would yield OOA(51219, 306, S5, 4, 1147), but