Best Known (94, 94+84, s)-Nets in Base 2
(94, 94+84, 53)-Net over F2 — Constructive and digital
Digital (94, 178, 53)-net over F2, using
- t-expansion [i] based on digital (90, 178, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 places 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 (90, 52)-sequence over F2, using
(94, 94+84, 60)-Net over F2 — Digital
Digital (94, 178, 60)-net over F2, using
- t-expansion [i] based on digital (92, 178, 60)-net over F2, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
(94, 94+84, 207)-Net over F2 — Upper bound on s (digital)
There is no digital (94, 178, 208)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2178, 208, F2, 84) (dual of [208, 30, 85]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
- adding a parity check bit [i] would yield linear OA(2180, 210, F2, 85) (dual of [210, 30, 86]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
(94, 94+84, 254)-Net in Base 2 — Upper bound on s
There is no (94, 178, 255)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 423390 231850 540274 865706 517653 905309 289082 614413 720591 > 2178 [i]