Best Known (130−16, 130, s)-Nets in Base 2
(130−16, 130, 8194)-Net over F2 — Constructive and digital
Digital (114, 130, 8194)-net over F2, using
- t-expansion [i] based on digital (113, 130, 8194)-net over F2, using
- net defined by OOA [i] based on linear OOA(2130, 8194, F2, 17, 17) (dual of [(8194, 17), 139168, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2130, 65553, F2, 17) (dual of [65553, 65423, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2129, 65536, F2, 17) (dual of [65536, 65407, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(2130, 65553, F2, 17) (dual of [65553, 65423, 18]-code), using
- net defined by OOA [i] based on linear OOA(2130, 8194, F2, 17, 17) (dual of [(8194, 17), 139168, 18]-NRT-code), using
(130−16, 130, 13762)-Net over F2 — Digital
Digital (114, 130, 13762)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2130, 13762, F2, 4, 16) (dual of [(13762, 4), 54918, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2130, 16388, F2, 4, 16) (dual of [(16388, 4), 65422, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(2130, 16388, F2, 4, 17) (dual of [(16388, 4), 65422, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2130, 65552, F2, 17) (dual of [65552, 65422, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2130, 65553, F2, 17) (dual of [65553, 65423, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2129, 65536, F2, 17) (dual of [65536, 65407, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2130, 65553, F2, 17) (dual of [65553, 65423, 18]-code), using
- OOA 4-folding [i] based on linear OA(2130, 65552, F2, 17) (dual of [65552, 65422, 18]-code), using
- strength reduction [i] based on linear OOA(2130, 16388, F2, 4, 17) (dual of [(16388, 4), 65422, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2130, 16388, F2, 4, 16) (dual of [(16388, 4), 65422, 17]-NRT-code), using
(130−16, 130, 293366)-Net in Base 2 — Upper bound on s
There is no (114, 130, 293367)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1361 149237 768375 106396 083448 304465 672070 > 2130 [i]