Best Known (18, 18+∞, s)-Nets in Base 25
(18, 18+∞, 126)-Net over F25 — Constructive and digital
Digital (18, m, 126)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 125)-sequence over F25, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
(18, 18+∞, 153)-Net over F25 — Digital
Digital (18, m, 153)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(18, 18+∞, 482)-Net in Base 25 — Upper bound on s
There is no (18, m, 483)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (18, 963, 483)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25963, 483, S25, 2, 945), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 119279 650449 992304 588949 877219 045948 523462 084901 421794 481335 558479 698097 403535 318298 680839 519163 056171 076244 146106 373325 542506 650745 897278 984637 628708 513539 997481 936866 963847 438459 665837 412106 307043 402521 559681 528007 638434 551724 349333 891938 931880 640923 084840 915069 875439 609521 814150 569712 133097 534641 655338 876719 307670 385406 059002 086316 496823 695570 079035 971241 524783 774944 776618 067453 691660 580457 452451 938832 355092 469962 107297 081616 129516 450596 379872 205212 487000 972833 627061 450823 805301 822507 905565 516374 830694 256924 153977 894695 832011 200390 433714 677253 696343 126162 398426 456736 720680 457861 009198 585220 196746 810644 015830 548099 121723 399005 739627 187171 892528 599000 060768 557006 314650 790011 590389 367640 840677 353927 551076 891153 323483 446249 838498 033736 949653 212423 165895 201825 714992 589878 436551 403231 936047 228316 614262 763904 858088 422903 582260 488719 750078 019110 345727 684470 111935 310967 607264 825478 915293 085442 041066 967457 262555 097197 344605 988742 800243 094814 683113 693295 777686 825100 540000 581956 638015 053659 378904 435541 615151 474397 533147 917073 971951 812437 745636 070516 603510 245746 332816 206142 093140 176284 895009 077980 488761 332164 772860 224641 432689 008133 419372 717949 441317 494779 226386 429374 356191 840286 201640 534115 724943 393256 260979 170890 479725 709453 630752 334911 970131 896166 197077 076824 849396 835799 893175 547895 522534 898077 489373 680037 942904 164083 302021 026611 328125 / 473 > 25963 [i]
- extracting embedded OOA [i] would yield OOA(25963, 483, S25, 2, 945), but