Best Known (80, 102, s)-Nets in Base 16
(80, 102, 95326)-Net over F16 — Constructive and digital
Digital (80, 102, 95326)-net over F16, using
- net defined by OOA [i] based on linear OOA(16102, 95326, F16, 22, 22) (dual of [(95326, 22), 2097070, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16102, 1048586, F16, 22) (dual of [1048586, 1048484, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16102, 1048586, F16, 22) (dual of [1048586, 1048484, 23]-code), using
(80, 102, 666829)-Net over F16 — Digital
Digital (80, 102, 666829)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16102, 666829, F16, 22) (dual of [666829, 666727, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
(80, 102, large)-Net in Base 16 — Upper bound on s
There is no (80, 102, large)-net in base 16, because
- 20 times m-reduction [i] would yield (80, 82, large)-net in base 16, but