Best Known (95, 95+∞, s)-Nets in Base 5
(95, 95+∞, 82)-Net over F5 — Constructive and digital
Digital (95, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 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
(95, 95+∞, 155)-Net over F5 — Digital
Digital (95, m, 155)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 154)-sequence over F5, using
- t-expansion [i] based on digital (94, 154)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 94 and N(F) ≥ 155, using
- t-expansion [i] based on digital (94, 154)-sequence over F5, using
(95, 95+∞, 398)-Net in Base 5 — Upper bound on s
There is no (95, m, 399)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (95, 1591, 399)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51591, 399, S5, 4, 1496), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 70819 362722 270958 047347 317163 872083 343481 337832 836950 337193 453876 139356 669862 490624 627585 326420 965339 572027 994075 798459 762219 358620 890607 420814 429447 704875 408073 801989 691933 599967 649933 814175 577910 692414 063580 206168 049864 138335 039272 519523 965514 046183 302301 134813 764169 384930 591879 883414 514313 072684 248059 472413 512294 512781 000016 308158 961638 413391 762813 625840 141795 199503 816275 828866 194532 261696 692610 331140 166620 877365 508468 359706 695675 658278 998248 211954 808073 746562 885119 590009 736634 491018 879067 005416 171593 072392 356042 944332 659007 125799 958244 829809 261525 247427 717294 302473 230184 427852 890235 096434 402689 688434 069002 110775 032939 411271 427511 387061 522352 643191 762406 884210 996608 948785 840658 238170 958323 710360 277533 279390 772479 364407 939590 761747 565780 789958 655414 824083 968410 850949 237584 102090 613185 848048 958980 330218 310093 608856 719540 074328 622418 465187 951655 988597 243441 439150 485857 755586 988031 652317 157726 085628 578700 443864 303843 092141 944853 896695 221615 693276 434638 456562 669038 650151 630657 373915 314486 330865 399377 378063 500002 227718 011781 151827 284573 602728 731770 785453 294362 980780 629612 809207 173995 673656 463623 046875 / 499 > 51591 [i]
- extracting embedded OOA [i] would yield OOA(51591, 399, S5, 4, 1496), but