Best Known (84, 108, s)-Nets in Base 7
(84, 108, 1403)-Net over F7 — Constructive and digital
Digital (84, 108, 1403)-net over F7, using
- net defined by OOA [i] based on linear OOA(7108, 1403, F7, 24, 24) (dual of [(1403, 24), 33564, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(7108, 16836, F7, 24) (dual of [16836, 16728, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(7108, 16839, F7, 24) (dual of [16839, 16731, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(7101, 16807, F7, 24) (dual of [16807, 16706, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(7108, 16839, F7, 24) (dual of [16839, 16731, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(7108, 16836, F7, 24) (dual of [16836, 16728, 25]-code), using
(84, 108, 16839)-Net over F7 — Digital
Digital (84, 108, 16839)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7108, 16839, F7, 24) (dual of [16839, 16731, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(7101, 16807, F7, 24) (dual of [16807, 16706, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
(84, 108, large)-Net in Base 7 — Upper bound on s
There is no (84, 108, large)-net in base 7, because
- 22 times m-reduction [i] would yield (84, 86, large)-net in base 7, but