Best Known (95−16, 95, s)-Nets in Base 7
(95−16, 95, 102945)-Net over F7 — Constructive and digital
Digital (79, 95, 102945)-net over F7, using
- net defined by OOA [i] based on linear OOA(795, 102945, F7, 16, 16) (dual of [(102945, 16), 1647025, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(795, 823560, F7, 16) (dual of [823560, 823465, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(73, 17, F7, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OA 8-folding and stacking [i] based on linear OA(795, 823560, F7, 16) (dual of [823560, 823465, 17]-code), using
(95−16, 95, 475914)-Net over F7 — Digital
Digital (79, 95, 475914)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(795, 475914, F7, 16) (dual of [475914, 475819, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(795, 823560, F7, 16) (dual of [823560, 823465, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(73, 17, F7, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(795, 823560, F7, 16) (dual of [823560, 823465, 17]-code), using
(95−16, 95, large)-Net in Base 7 — Upper bound on s
There is no (79, 95, large)-net in base 7, because
- 14 times m-reduction [i] would yield (79, 81, large)-net in base 7, but