Best Known (85, 100, s)-Nets in Base 5
(85, 100, 55807)-Net over F5 — Constructive and digital
Digital (85, 100, 55807)-net over F5, using
- net defined by OOA [i] based on linear OOA(5100, 55807, F5, 15, 15) (dual of [(55807, 15), 837005, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5100, 390650, F5, 15) (dual of [390650, 390550, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 390652, F5, 15) (dual of [390652, 390552, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(53, 27, F5, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(5100, 390652, F5, 15) (dual of [390652, 390552, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5100, 390650, F5, 15) (dual of [390650, 390550, 16]-code), using
(85, 100, 298029)-Net over F5 — Digital
Digital (85, 100, 298029)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5100, 298029, F5, 15) (dual of [298029, 297929, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 390652, F5, 15) (dual of [390652, 390552, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(53, 27, F5, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(5100, 390652, F5, 15) (dual of [390652, 390552, 16]-code), using
(85, 100, large)-Net in Base 5 — Upper bound on s
There is no (85, 100, large)-net in base 5, because
- 13 times m-reduction [i] would yield (85, 87, large)-net in base 5, but