Best Known (47, 47+∞, s)-Nets in Base 5
(47, 47+∞, 78)-Net over F5 — Constructive and digital
Digital (47, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (47, 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
(47, 47+∞, 92)-Net over F5 — Digital
Digital (47, m, 92)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (47, 91)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 47 and N(F) ≥ 92, using
(47, 47+∞, 205)-Net in Base 5 — Upper bound on s
There is no (47, m, 206)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (47, 614, 206)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5614, 206, S5, 3, 567), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 125026 360189 053436 284157 564056 740270 749899 549031 580400 149887 388951 720170 589063 835562 398032 107000 904362 091932 158172 035863 597505 672439 217565 568869 518549 881820 653639 048917 561703 518662 796773 247127 870234 925512 527479 695769 367162 817105 964695 992572 330600 826980 252148 217406 395678 940336 247213 416576 551022 811197 430611 468091 268887 988119 798048 166782 505067 480712 270371 683904 912826 585867 757945 772799 839140 483613 153520 536798 168905 079364 776611 328125 / 71 > 5614 [i]
- extracting embedded OOA [i] would yield OOA(5614, 206, S5, 3, 567), but