Best Known (28, ∞, s)-Nets in Base 2
(28, ∞, 21)-Net over F2 — Constructive and digital
Digital (28, m, 21)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 20)-sequence over F2, using
- t-expansion [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- t-expansion [i] based on digital (21, 20)-sequence over F2, using
(28, ∞, 25)-Net over F2 — Digital
Digital (28, m, 25)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
(28, ∞, 35)-Net in Base 2 — Upper bound on s
There is no (28, m, 36)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (28, 209, 36)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2209, 36, S2, 6, 181), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 75693 209636 775477 939128 582397 638123 229205 849819 144673 714036 015104 / 91 > 2209 [i]
- extracting embedded OOA [i] would yield OOA(2209, 36, S2, 6, 181), but