Best Known (97−16, 97, s)-Nets in Base 2
(97−16, 97, 513)-Net over F2 — Constructive and digital
Digital (81, 97, 513)-net over F2, using
- net defined by OOA [i] based on linear OOA(297, 513, F2, 16, 16) (dual of [(513, 16), 8111, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(297, 4104, F2, 16) (dual of [4104, 4007, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-code), using
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(297, 4104, F2, 16) (dual of [4104, 4007, 17]-code), using
(97−16, 97, 1189)-Net over F2 — Digital
Digital (81, 97, 1189)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(297, 1189, F2, 3, 16) (dual of [(1189, 3), 3470, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(297, 1369, F2, 3, 16) (dual of [(1369, 3), 4010, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(297, 4107, F2, 16) (dual of [4107, 4010, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-code), using
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-code), using
- OOA 3-folding [i] based on linear OA(297, 4107, F2, 16) (dual of [4107, 4010, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(297, 1369, F2, 3, 16) (dual of [(1369, 3), 4010, 17]-NRT-code), using
(97−16, 97, 16802)-Net in Base 2 — Upper bound on s
There is no (81, 97, 16803)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 158471 225643 286069 172112 178876 > 297 [i]