Best Known (69, ∞, s)-Nets in Base 5
(69, ∞, 82)-Net over F5 — Constructive and digital
Digital (69, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (69, 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
(69, ∞, 132)-Net over F5 — Digital
Digital (69, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (69, 131)-sequence over F5, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
(69, ∞, 293)-Net in Base 5 — Upper bound on s
There is no (69, m, 294)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (69, 1171, 294)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51171, 294, S5, 4, 1102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 372600 113421 784674 222488 530177 936512 518776 328515 388371 747949 041593 527314 719198 628829 042713 495985 687621 709396 219508 238394 075899 798609 944548 606540 594556 314653 634436 634265 499855 966530 217193 918722 953404 168767 599848 548537 474006 224762 283963 477673 649370 378013 461110 226162 163691 807241 673048 199819 544289 465334 663537 278076 424985 973474 476656 624027 992669 604036 327509 292302 982352 539995 722271 408516 803203 881681 464352 110309 632874 559044 798268 717271 768635 358916 951960 990844 156298 359222 546496 842546 999052 979791 017595 622989 508511 579158 314090 842092 422757 521045 087844 986547 976326 201095 017538 151958 666401 776428 980235 385618 207514 558299 069482 656095 188307 928651 072601 110541 281273 495670 759069 031093 988320 672202 816299 707344 586469 607665 919593 006759 209946 876344 859158 116420 140284 953037 140308 621920 327928 448714 825682 142048 890455 043874 680995 941162 109375 / 1103 > 51171 [i]
- extracting embedded OOA [i] would yield OOA(51171, 294, S5, 4, 1102), but