Best Known (88, 104, s)-Nets in Base 5
(88, 104, 48833)-Net over F5 — Constructive and digital
Digital (88, 104, 48833)-net over F5, using
- net defined by OOA [i] based on linear OOA(5104, 48833, F5, 16, 16) (dual of [(48833, 16), 781224, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5104, 390664, F5, 16) (dual of [390664, 390560, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(57, 39, F5, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OA 8-folding and stacking [i] based on linear OA(5104, 390664, F5, 16) (dual of [390664, 390560, 17]-code), using
(88, 104, 209797)-Net over F5 — Digital
Digital (88, 104, 209797)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5104, 209797, F5, 16) (dual of [209797, 209693, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5104, 390658, F5, 16) (dual of [390658, 390554, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [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(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(55, 31, F5, 3) (dual of [31, 26, 4]-code or 31-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(5104, 390658, F5, 16) (dual of [390658, 390554, 17]-code), using
(88, 104, large)-Net in Base 5 — Upper bound on s
There is no (88, 104, large)-net in base 5, because
- 14 times m-reduction [i] would yield (88, 90, large)-net in base 5, but