Best Known (72, 213, s)-Nets in Base 2
(72, 213, 49)-Net over F2 — Constructive and digital
Digital (72, 213, 49)-net over F2, using
- t-expansion [i] based on digital (70, 213, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
(72, 213, 105)-Net in Base 2 — Upper bound on s
There is no (72, 213, 106)-net in base 2, because
- 8 times m-reduction [i] would yield (72, 205, 106)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2205, 106, S2, 2, 133), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4936 513671 963618 126464 907547 672051 514948 207596 900739 590045 827072 / 67 > 2205 [i]
- extracting embedded OOA [i] would yield OOA(2205, 106, S2, 2, 133), but