Best Known (44, 44+∞, s)-Nets in Base 5
(44, 44+∞, 78)-Net over F5 — Constructive and digital
Digital (44, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 77)-sequence over F5, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
(44, 44+∞, 84)-Net over F5 — Digital
Digital (44, m, 84)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 83)-sequence over F5, using
- t-expansion [i] based on digital (43, 83)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 43 and N(F) ≥ 84, using
- t-expansion [i] based on digital (43, 83)-sequence over F5, using
(44, 44+∞, 192)-Net in Base 5 — Upper bound on s
There is no (44, m, 193)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (44, 575, 193)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5575, 193, S5, 3, 531), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 109 165714 522709 262479 026187 402824 002886 769745 890983 377510 668916 766288 460060 885806 553706 733261 754918 668765 605275 479258 471522 190319 421176 890598 172731 349091 460804 160456 125859 661931 045877 612504 470829 717885 716021 776693 120779 001364 525089 045587 609383 972264 670794 617897 732815 204304 417303 790493 168001 467731 839695 593698 543682 110195 832980 833649 137073 286506 662945 316682 448364 080382 230412 169519 695453 345775 604248 046875 / 133 > 5575 [i]
- extracting embedded OOA [i] would yield OOA(5575, 193, S5, 3, 531), but