Best Known (152−76, 152, s)-Nets in Base 2
(152−76, 152, 50)-Net over F2 — Constructive and digital
Digital (76, 152, 50)-net over F2, using
- t-expansion [i] based on digital (75, 152, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [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 (75, 49)-sequence over F2, using
(152−76, 152, 163)-Net over F2 — Upper bound on s (digital)
There is no digital (76, 152, 164)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2152, 164, F2, 76) (dual of [164, 12, 77]-code), but
- residual code [i] would yield linear OA(276, 87, F2, 38) (dual of [87, 11, 39]-code), but
(152−76, 152, 189)-Net in Base 2 — Upper bound on s
There is no (76, 152, 190)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6410 402796 969589 145025 833505 056272 552890 346572 > 2152 [i]