Best Known (88, 103, s)-Nets in Base 7
(88, 103, 823548)-Net over F7 — Constructive and digital
Digital (88, 103, 823548)-net over F7, using
- net defined by OOA [i] based on linear OOA(7103, 823548, F7, 15, 15) (dual of [(823548, 15), 12353117, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(7103, 5764837, F7, 15) (dual of [5764837, 5764734, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(7103, 5764839, F7, 15) (dual of [5764839, 5764736, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(76, 38, F7, 4) (dual of [38, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(7103, 5764839, F7, 15) (dual of [5764839, 5764736, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(7103, 5764837, F7, 15) (dual of [5764837, 5764734, 16]-code), using
(88, 103, 4036671)-Net over F7 — Digital
Digital (88, 103, 4036671)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7103, 4036671, F7, 15) (dual of [4036671, 4036568, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(7103, 5764839, F7, 15) (dual of [5764839, 5764736, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(76, 38, F7, 4) (dual of [38, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(7103, 5764839, F7, 15) (dual of [5764839, 5764736, 16]-code), using
(88, 103, large)-Net in Base 7 — Upper bound on s
There is no (88, 103, large)-net in base 7, because
- 13 times m-reduction [i] would yield (88, 90, large)-net in base 7, but