Best Known (46, 46+∞, s)-Nets in Base 7
(46, 46+∞, 47)-Net over F7 — Constructive and digital
Digital (46, m, 47)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 46)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F49, using
(46, 46+∞, 105)-Net over F7 — Digital
Digital (46, m, 105)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
(46, 46+∞, 296)-Net in Base 7 — Upper bound on s
There is no (46, m, 297)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (46, 887, 297)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7887, 297, S7, 3, 841), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 170 761266 679752 642660 079622 926530 943644 913568 305728 842451 915264 909937 736209 423973 056039 245910 975560 864609 847444 380313 060026 050097 303419 586431 099231 393790 002718 307580 943651 821039 462850 543021 853402 427885 974221 561300 364259 729931 981371 255793 051247 197379 386556 752043 535319 104784 929916 576112 111680 488830 057707 366989 514974 283700 277899 836838 414094 237575 037373 632717 020070 722806 831000 585522 302284 497318 571082 371117 398426 363368 343476 919900 261273 400949 405172 559498 432879 460220 803607 296085 687789 201392 227360 549006 010463 446453 347685 531794 121586 768904 589553 462381 425915 523163 005179 814883 394066 356766 127847 406180 147798 682002 957515 649840 302594 200766 935054 806011 929019 020165 423698 349045 997242 989309 209688 127530 849751 580076 332966 347368 101581 212786 182090 565326 343404 660861 / 421 > 7887 [i]
- extracting embedded OOA [i] would yield OOA(7887, 297, S7, 3, 841), but