Best Known (46, 46+12, s)-Nets in Base 5
(46, 46+12, 2606)-Net over F5 — Constructive and digital
Digital (46, 58, 2606)-net over F5, using
- net defined by OOA [i] based on linear OOA(558, 2606, F5, 12, 12) (dual of [(2606, 12), 31214, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(558, 15636, F5, 12) (dual of [15636, 15578, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(558, 15640, F5, 12) (dual of [15640, 15582, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(53, 15, F5, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(558, 15640, F5, 12) (dual of [15640, 15582, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(558, 15636, F5, 12) (dual of [15636, 15578, 13]-code), using
(46, 46+12, 10909)-Net over F5 — Digital
Digital (46, 58, 10909)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(558, 10909, F5, 12) (dual of [10909, 10851, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(558, 15640, F5, 12) (dual of [15640, 15582, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(53, 15, F5, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(558, 15640, F5, 12) (dual of [15640, 15582, 13]-code), using
(46, 46+12, 4274366)-Net in Base 5 — Upper bound on s
There is no (46, 58, 4274367)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 34694 508504 962798 185661 574952 884777 527273 > 558 [i]