Best Known (148−70, 148, s)-Nets in Base 2
(148−70, 148, 50)-Net over F2 — Constructive and digital
Digital (78, 148, 50)-net over F2, using
- t-expansion [i] based on digital (75, 148, 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
(148−70, 148, 52)-Net over F2 — Digital
Digital (78, 148, 52)-net over F2, using
- t-expansion [i] based on digital (77, 148, 52)-net over F2, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 77 and N(F) ≥ 52, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
(148−70, 148, 175)-Net over F2 — Upper bound on s (digital)
There is no digital (78, 148, 176)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2148, 176, F2, 70) (dual of [176, 28, 71]-code), but
- adding a parity check bit [i] would yield linear OA(2149, 177, F2, 71) (dual of [177, 28, 72]-code), but
(148−70, 148, 213)-Net in Base 2 — Upper bound on s
There is no (78, 148, 214)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 408 441617 355578 995683 142262 066645 952028 781580 > 2148 [i]