Best Known (101, 101+21, s)-Nets in Base 8
(101, 101+21, 52429)-Net over F8 — Constructive and digital
Digital (101, 122, 52429)-net over F8, using
- net defined by OOA [i] based on linear OOA(8122, 52429, F8, 21, 21) (dual of [(52429, 21), 1100887, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8122, 524291, F8, 21) (dual of [524291, 524169, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8122, 524294, F8, 21) (dual of [524294, 524172, 22]-code), using
- trace code [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8122, 524294, F8, 21) (dual of [524294, 524172, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8122, 524291, F8, 21) (dual of [524291, 524169, 22]-code), using
(101, 101+21, 524294)-Net over F8 — Digital
Digital (101, 122, 524294)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8122, 524294, F8, 21) (dual of [524294, 524172, 22]-code), using
- trace code [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
(101, 101+21, large)-Net in Base 8 — Upper bound on s
There is no (101, 122, large)-net in base 8, because
- 19 times m-reduction [i] would yield (101, 103, large)-net in base 8, but