Best Known (60−13, 60, s)-Nets in Base 7
(60−13, 60, 2805)-Net over F7 — Constructive and digital
Digital (47, 60, 2805)-net over F7, using
- net defined by OOA [i] based on linear OOA(760, 2805, F7, 13, 13) (dual of [(2805, 13), 36405, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(760, 16831, F7, 13) (dual of [16831, 16771, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- OOA 6-folding and stacking with additional row [i] based on linear OA(760, 16831, F7, 13) (dual of [16831, 16771, 14]-code), using
(60−13, 60, 16831)-Net over F7 — Digital
Digital (47, 60, 16831)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(760, 16831, F7, 13) (dual of [16831, 16771, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
(60−13, 60, large)-Net in Base 7 — Upper bound on s
There is no (47, 60, large)-net in base 7, because
- 11 times m-reduction [i] would yield (47, 49, large)-net in base 7, but