Best Known (151−76, 151, s)-Nets in Base 2
(151−76, 151, 50)-Net over F2 — Constructive and digital
Digital (75, 151, 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]
(151−76, 151, 161)-Net over F2 — Upper bound on s (digital)
There is no digital (75, 151, 162)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2151, 162, F2, 76) (dual of [162, 11, 77]-code), but
- residual code [i] would yield linear OA(275, 85, F2, 38) (dual of [85, 10, 39]-code), but
(151−76, 151, 185)-Net in Base 2 — Upper bound on s
There is no (75, 151, 186)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3350 345185 926612 120137 893371 623361 909991 309316 > 2151 [i]