Best Known (93, ∞, s)-Nets in Base 2
(93, ∞, 53)-Net over F2 — Constructive and digital
Digital (93, m, 53)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 52)-sequence over F2, using
- t-expansion [i] based on digital (90, 52)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (90, 52)-sequence over F2, using
(93, ∞, 60)-Net over F2 — Digital
Digital (93, m, 60)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 59)-sequence over F2, using
- t-expansion [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
- t-expansion [i] based on digital (92, 59)-sequence over F2, using
(93, ∞, 102)-Net in Base 2 — Upper bound on s
There is no (93, m, 103)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (93, 815, 103)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2815, 103, S2, 8, 722), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 178 730952 494144 579049 793741 285293 715556 414662 497219 801094 689223 148273 089266 805081 194644 489512 974136 437234 619739 846357 505957 463318 628585 984351 837397 018431 290661 464929 076591 457364 305446 105116 307365 176717 580669 918918 116082 709124 079463 175685 789894 836224 / 723 > 2815 [i]
- extracting embedded OOA [i] would yield OOA(2815, 103, S2, 8, 722), but