Best Known (199, 199+∞, s)-Nets in Base 2
(199, 199+∞, 66)-Net over F2 — Constructive and digital
Digital (199, m, 66)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (199, 65)-sequence over F2, using
- t-expansion [i] based on digital (163, 65)-sequence over F2, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second 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) = 49 and N(F) ≥ 66, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
- t-expansion [i] based on digital (163, 65)-sequence over F2, using
(199, 199+∞, 91)-Net over F2 — Digital
Digital (199, m, 91)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (199, 90)-sequence over F2, using
- t-expansion [i] based on digital (190, 90)-sequence over F2, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
- t-expansion [i] based on digital (190, 90)-sequence over F2, using
(199, 199+∞, 210)-Net in Base 2 — Upper bound on s
There is no (199, m, 211)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (199, 1467, 211)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21467, 211, S2, 7, 1268), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 651187 659339 130579 810191 613741 767064 556157 912404 493788 783543 797478 859076 413749 476180 109189 245104 493821 035158 238942 446662 185673 571074 663696 318482 731296 506940 093787 826562 238695 804231 678232 493893 942652 286860 015227 361660 911030 914371 141131 376991 375804 125822 199593 720025 870989 170025 094855 159104 547444 554237 142816 478459 506905 458500 463915 622616 021257 480489 312788 214270 457151 821244 754668 586059 246887 129006 624250 006145 338087 516198 971848 134791 278836 580352 / 1269 > 21467 [i]
- extracting embedded OOA [i] would yield OOA(21467, 211, S2, 7, 1268), but