Best Known (49−24, 49, s)-Nets in Base 2
(49−24, 49, 21)-Net over F2 — Constructive and digital
Digital (25, 49, 21)-net over F2, using
- t-expansion [i] based on digital (21, 49, 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
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(49−24, 49, 24)-Net over F2 — Digital
Digital (25, 49, 24)-net over F2, using
- net from sequence [i] based on digital (25, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 25 and N(F) ≥ 24, using
(49−24, 49, 59)-Net over F2 — Upper bound on s (digital)
There is no digital (25, 49, 60)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(249, 60, F2, 24) (dual of [60, 11, 25]-code), but
- construction Y1 [i] would yield
- linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- linear OA(211, 60, F2, 4) (dual of [60, 49, 5]-code), but
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code), but
- construction Y1 [i] would yield
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- “BoV†bound on codes from Brouwer’s database [i]
- linear OA(247, 58, F2, 24) (dual of [58, 11, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- discarding factors / shortening the dual code would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code), but
- linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- construction Y1 [i] would yield
(49−24, 49, 66)-Net in Base 2 — Upper bound on s
There is no (25, 49, 67)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(249, 67, S2, 24), but
- the linear programming bound shows that M ≥ 3 474527 112516 337664 / 5681 > 249 [i]