Best Known (76−14, 76, s)-Nets in Base 7
(76−14, 76, 16810)-Net over F7 — Constructive and digital
Digital (62, 76, 16810)-net over F7, using
- net defined by OOA [i] based on linear OOA(776, 16810, F7, 14, 14) (dual of [(16810, 14), 235264, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(776, 117670, F7, 14) (dual of [117670, 117594, 15]-code), using
- 1 times truncation [i] based on linear OA(777, 117671, F7, 15) (dual of [117671, 117594, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(74, 22, F7, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(777, 117671, F7, 15) (dual of [117671, 117594, 16]-code), using
- OA 7-folding and stacking [i] based on linear OA(776, 117670, F7, 14) (dual of [117670, 117594, 15]-code), using
(76−14, 76, 117670)-Net over F7 — Digital
Digital (62, 76, 117670)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(776, 117670, F7, 14) (dual of [117670, 117594, 15]-code), using
- 1 times truncation [i] based on linear OA(777, 117671, F7, 15) (dual of [117671, 117594, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(74, 22, F7, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(777, 117671, F7, 15) (dual of [117671, 117594, 16]-code), using
(76−14, 76, large)-Net in Base 7 — Upper bound on s
There is no (62, 76, large)-net in base 7, because
- 12 times m-reduction [i] would yield (62, 64, large)-net in base 7, but