Best Known (82−46, 82, s)-Nets in Base 2
(82−46, 82, 24)-Net over F2 — Constructive and digital
Digital (36, 82, 24)-net over F2, using
- t-expansion [i] based on digital (33, 82, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(82−46, 82, 30)-Net over F2 — Digital
Digital (36, 82, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
(82−46, 82, 80)-Net over F2 — Upper bound on s (digital)
There is no digital (36, 82, 81)-net over F2, because
- 6 times m-reduction [i] would yield digital (36, 76, 81)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(276, 81, F2, 40) (dual of [81, 5, 41]-code), but
(82−46, 82, 81)-Net in Base 2 — Upper bound on s
There is no (36, 82, 82)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5 182006 168259 571074 231840 > 282 [i]