Best Known (253−182, 253, s)-Nets in Base 2
(253−182, 253, 49)-Net over F2 — Constructive and digital
Digital (71, 253, 49)-net over F2, using
- t-expansion [i] based on digital (70, 253, 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
(253−182, 253, 104)-Net in Base 2 — Upper bound on s
There is no (71, 253, 105)-net in base 2, because
- 51 times m-reduction [i] would yield (71, 202, 105)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2202, 105, S2, 2, 131), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 102 844034 832575 377634 685573 909834 406561 420991 602098 741459 288064 / 11 > 2202 [i]
- extracting embedded OOA [i] would yield OOA(2202, 105, S2, 2, 131), but