Best Known (21, 44, s)-Nets in Base 2
(21, 44, 21)-Net over F2 — Constructive and digital
Digital (21, 44, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
(21, 44, 51)-Net over F2 — Upper bound on s (digital)
There is no digital (21, 44, 52)-net over F2, because
- 1 times m-reduction [i] would yield digital (21, 43, 52)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(243, 52, F2, 22) (dual of [52, 9, 23]-code), but
- adding a parity check bit [i] would yield linear OA(244, 53, F2, 23) (dual of [53, 9, 24]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(244, 53, F2, 23) (dual of [53, 9, 24]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(243, 52, F2, 22) (dual of [52, 9, 23]-code), but
(21, 44, 53)-Net in Base 2 — Upper bound on s
There is no (21, 44, 54)-net in base 2, because
- 1 times m-reduction [i] would yield (21, 43, 54)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(243, 54, S2, 22), but
- the linear programming bound shows that M ≥ 2146 246697 418752 / 243 > 243 [i]
- extracting embedded orthogonal array [i] would yield OA(243, 54, S2, 22), but