Best Known (32, 38, s)-Nets in Base 7
(32, 38, 274520)-Net over F7 — Constructive and digital
Digital (32, 38, 274520)-net over F7, using
- net defined by OOA [i] based on linear OOA(738, 274520, F7, 6, 6) (dual of [(274520, 6), 1647082, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(738, 823560, F7, 6) (dual of [823560, 823522, 7]-code), using
- 1 times code embedding in larger space [i] based on linear OA(737, 823559, F7, 6) (dual of [823559, 823522, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(722, 823543, F7, 4) (dual of [823543, 823521, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(737, 823559, F7, 6) (dual of [823559, 823522, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(738, 823560, F7, 6) (dual of [823560, 823522, 7]-code), using
(32, 38, 1149294)-Net over F7 — Digital
Digital (32, 38, 1149294)-net over F7, using
(32, 38, large)-Net in Base 7 — Upper bound on s
There is no (32, 38, large)-net in base 7, because
- 4 times m-reduction [i] would yield (32, 34, large)-net in base 7, but