Best Known (249, ∞, s)-Nets in Base 2
(249, ∞, 104)-Net over F2 — Constructive and digital
Digital (249, m, 104)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (249, 103)-sequence over F2, using
- base reduction for sequences [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- base reduction for sequences [i] based on digital (73, 103)-sequence over F4, using
(249, ∞, 129)-Net over F2 — Digital
Digital (249, m, 129)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (249, 128)-sequence over F2, using
- t-expansion [i] based on digital (215, 128)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 215 and N(F) ≥ 129, using
- t-expansion [i] based on digital (215, 128)-sequence over F2, using
(249, ∞, 260)-Net in Base 2 — Upper bound on s
There is no (249, m, 261)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (249, 2077, 261)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(22077, 261, S2, 8, 1828), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 34838 921529 409469 270548 295832 426064 569407 625157 226067 679245 321751 920784 545834 098392 545330 444245 203671 176462 918748 166858 997577 906687 189308 160528 350304 951792 129213 068736 266433 858575 019599 603538 090932 148291 546231 687793 970483 369190 674484 125863 706110 194568 263743 857119 846276 134385 980580 617092 927261 446063 748634 256120 782258 788855 100826 231597 346730 949354 355590 131718 975779 304570 497889 158686 359908 659100 918259 949541 258665 095550 505594 862349 775720 967530 555882 942131 207866 594650 418585 742559 584544 458135 995208 104341 806913 592232 853918 427695 921343 647698 601722 313666 005530 756288 537984 092469 846273 788823 299040 214203 235171 424981 899125 730549 170176 / 1829 > 22077 [i]
- extracting embedded OOA [i] would yield OOA(22077, 261, S2, 8, 1828), but