Best Known (116−21, 116, s)-Nets in Base 9
(116−21, 116, 53147)-Net over F9 — Constructive and digital
Digital (95, 116, 53147)-net over F9, using
- 91 times duplication [i] based on digital (94, 115, 53147)-net over F9, using
- net defined by OOA [i] based on linear OOA(9115, 53147, F9, 21, 21) (dual of [(53147, 21), 1115972, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9115, 531471, F9, 21) (dual of [531471, 531356, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(985, 531441, F9, 16) (dual of [531441, 531356, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(96, 30, F9, 4) (dual of [30, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(9115, 531471, F9, 21) (dual of [531471, 531356, 22]-code), using
- net defined by OOA [i] based on linear OOA(9115, 53147, F9, 21, 21) (dual of [(53147, 21), 1115972, 22]-NRT-code), using
(116−21, 116, 531478)-Net over F9 — Digital
Digital (95, 116, 531478)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9116, 531478, F9, 21) (dual of [531478, 531362, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(979, 531441, F9, 15) (dual of [531441, 531362, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
(116−21, 116, large)-Net in Base 9 — Upper bound on s
There is no (95, 116, large)-net in base 9, because
- 19 times m-reduction [i] would yield (95, 97, large)-net in base 9, but