Best Known (52, 52+∞, s)-Nets in Base 5
(52, 52+∞, 82)-Net over F5 — Constructive and digital
Digital (52, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (52, 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
(52, 52+∞, 104)-Net over F5 — Digital
Digital (52, m, 104)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (52, 103)-sequence over F5, using
- t-expansion [i] based on digital (51, 103)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 51 and N(F) ≥ 104, using
- t-expansion [i] based on digital (51, 103)-sequence over F5, using
(52, 52+∞, 225)-Net in Base 5 — Upper bound on s
There is no (52, m, 226)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (52, 674, 226)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5674, 226, S5, 3, 622), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 835649 624700 020062 177217 324018 381853 455898 650567 538563 769517 942853 186199 273725 071438 568612 235270 249570 143437 730907 528303 704326 921452 195385 375097 225793 744119 745840 935200 099549 943022 586068 002334 592928 557325 366439 548311 045726 961033 280193 294306 554030 354077 387301 456174 418851 187345 118793 518120 933504 347911 459226 889411 591585 536048 183391 468440 783343 123520 672835 699376 574953 457534 585381 169369 680839 029948 604066 527311 845113 905493 413267 370323 392613 240542 914354 591630 399227 142333 984375 / 623 > 5674 [i]
- extracting embedded OOA [i] would yield OOA(5674, 226, S5, 3, 622), but