Best Known (76, 76+∞, s)-Nets in Base 5
(76, 76+∞, 82)-Net over F5 — Constructive and digital
Digital (76, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (76, 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
(76, 76+∞, 150)-Net over F5 — Digital
Digital (76, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [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
(76, 76+∞, 322)-Net in Base 5 — Upper bound on s
There is no (76, m, 323)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (76, 1287, 323)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51287, 323, S5, 4, 1211), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 182 027631 864399 231932 992695 666200 052688 124049 009769 638609 962428 138896 120118 864794 249394 568363 451950 532487 131261 960416 911923 939565 491903 648807 132459 237999 595827 844783 215229 401351 692820 552396 832740 721333 711121 654765 136427 334480 141901 322106 874824 901332 228945 160320 472106 970884 409813 249364 716265 164183 992729 051155 027445 811829 991989 309446 240873 987133 639474 036312 937530 274939 308668 992061 389734 776490 258743 652352 513611 153632 009110 227844 373390 172165 865942 553535 842308 614717 627993 982533 933174 400054 660467 918537 600183 376441 248302 886065 751620 297827 619427 263347 306033 664482 543849 974862 293696 687841 021654 121522 736558 258785 509410 975155 655117 035250 974177 585867 429124 477044 942478 225671 277068 892786 356972 987856 202239 491441 228607 554937 600010 853163 480517 041613 831429 823025 787670 254480 832069 327855 832210 293905 528115 834208 139940 951311 134655 573541 000214 690146 298297 683926 898667 857428 339156 289354 150430 881418 287754 058837 890625 / 303 > 51287 [i]
- extracting embedded OOA [i] would yield OOA(51287, 323, S5, 4, 1211), but