Best Known (164−105, 164, s)-Nets in Base 2
(164−105, 164, 43)-Net over F2 — Constructive and digital
Digital (59, 164, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(164−105, 164, 112)-Net in Base 2 — Upper bound on s
There is no (59, 164, 113)-net in base 2, because
- 1 times m-reduction [i] would yield (59, 163, 113)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 12 710730 407787 613963 214880 469107 787189 141073 117568 > 2163 [i]