Best Known (83, 83+24, s)-Nets in Base 8
(83, 83+24, 2731)-Net over F8 — Constructive and digital
Digital (83, 107, 2731)-net over F8, using
- t-expansion [i] based on digital (82, 107, 2731)-net over F8, using
- net defined by OOA [i] based on linear OOA(8107, 2731, F8, 25, 25) (dual of [(2731, 25), 68168, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8107, 32773, F8, 25) (dual of [32773, 32666, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 6, F8, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8107, 32774, F8, 25) (dual of [32774, 32667, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8107, 32773, F8, 25) (dual of [32773, 32666, 26]-code), using
- net defined by OOA [i] based on linear OOA(8107, 2731, F8, 25, 25) (dual of [(2731, 25), 68168, 26]-NRT-code), using
(83, 83+24, 29028)-Net over F8 — Digital
Digital (83, 107, 29028)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8107, 29028, F8, 24) (dual of [29028, 28921, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8107, 32779, F8, 24) (dual of [32779, 32672, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8107, 32779, F8, 24) (dual of [32779, 32672, 25]-code), using
(83, 83+24, large)-Net in Base 8 — Upper bound on s
There is no (83, 107, large)-net in base 8, because
- 22 times m-reduction [i] would yield (83, 85, large)-net in base 8, but