Best Known (143, ∞, s)-Nets in Base 3
(143, ∞, 80)-Net over F3 — Constructive and digital
Digital (143, m, 80)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 79)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 79)-sequence over F9, using
- s-reduction based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- s-reduction based on digital (32, 80)-sequence over F9, using
- base reduction for sequences [i] based on digital (32, 79)-sequence over F9, using
(143, ∞, 120)-Net over F3 — Digital
Digital (143, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(143, ∞, 299)-Net in Base 3 — Upper bound on s
There is no (143, m, 300)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (143, 1793, 300)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31793, 300, S3, 6, 1650), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 226482 863797 803009 676130 914900 852210 550415 531873 758932 634008 062768 526605 299087 152260 955345 430415 817007 670575 618298 282956 390419 203689 517540 134570 675300 831862 797474 985786 777348 560972 307249 485514 991691 096879 321232 721593 169540 440777 216654 698178 965534 271457 444582 846765 569886 262050 897203 053668 894228 508896 117663 957659 659757 716568 453046 943754 461935 723429 536433 102666 755598 390279 752499 808149 196551 683075 542251 086395 517067 961727 047103 403304 599364 975816 477804 487533 179652 328381 180090 247596 225847 325849 846848 761423 234513 623721 401718 006565 462654 141260 935888 862687 608746 340176 486426 713167 851260 443937 973352 467134 611716 963494 986882 734889 208653 802517 420841 080300 303288 027905 836785 764120 496918 177164 892730 144587 232600 765222 836993 313850 588119 861333 253477 100963 682601 914474 150311 407134 348168 842406 388499 158673 155080 680381 629562 958220 534907 664245 376303 390866 163895 654557 890651 / 1651 > 31793 [i]
- extracting embedded OOA [i] would yield OOA(31793, 300, S3, 6, 1650), but