Best Known (63, 63+14, s)-Nets in Base 7
(63, 63+14, 16811)-Net over F7 — Constructive and digital
Digital (63, 77, 16811)-net over F7, using
- net defined by OOA [i] based on linear OOA(777, 16811, F7, 14, 14) (dual of [(16811, 14), 235277, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(777, 117677, F7, 14) (dual of [117677, 117600, 15]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [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(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- OA 7-folding and stacking [i] based on linear OA(777, 117677, F7, 14) (dual of [117677, 117600, 15]-code), using
(63, 63+14, 117677)-Net over F7 — Digital
Digital (63, 77, 117677)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(777, 117677, F7, 14) (dual of [117677, 117600, 15]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [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(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
(63, 63+14, large)-Net in Base 7 — Upper bound on s
There is no (63, 77, large)-net in base 7, because
- 12 times m-reduction [i] would yield (63, 65, large)-net in base 7, but