Best Known (74, 146, s)-Nets in Base 2
(74, 146, 49)-Net over F2 — Constructive and digital
Digital (74, 146, 49)-net over F2, using
- t-expansion [i] based on digital (70, 146, 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
(74, 146, 164)-Net over F2 — Upper bound on s (digital)
There is no digital (74, 146, 165)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2146, 165, F2, 72) (dual of [165, 19, 73]-code), but
- residual code [i] would yield linear OA(274, 92, F2, 36) (dual of [92, 18, 37]-code), but
- adding a parity check bit [i] would yield linear OA(275, 93, F2, 37) (dual of [93, 18, 38]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(275, 93, F2, 37) (dual of [93, 18, 38]-code), but
- residual code [i] would yield linear OA(274, 92, F2, 36) (dual of [92, 18, 37]-code), but
(74, 146, 188)-Net in Base 2 — Upper bound on s
There is no (74, 146, 189)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 91 073635 319581 095339 936202 649448 755815 833125 > 2146 [i]