Best Known (76, 150, s)-Nets in Base 2
(76, 150, 50)-Net over F2 — Constructive and digital
Digital (76, 150, 50)-net over F2, using
- t-expansion [i] based on digital (75, 150, 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
(76, 150, 171)-Net over F2 — Upper bound on s (digital)
There is no digital (76, 150, 172)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2150, 172, F2, 74) (dual of [172, 22, 75]-code), but
- residual code [i] would yield OA(276, 97, S2, 37), but
- 1 times truncation [i] would yield OA(275, 96, S2, 36), but
- the linear programming bound shows that M ≥ 22708 462595 641194 417680 809984 / 528333 > 275 [i]
- 1 times truncation [i] would yield OA(275, 96, S2, 36), but
- residual code [i] would yield OA(276, 97, S2, 37), but
(76, 150, 193)-Net in Base 2 — Upper bound on s
There is no (76, 150, 194)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1553 318069 109826 304669 218191 812773 779895 026864 > 2150 [i]