Best Known (95, 114, s)-Nets in Base 5
(95, 114, 8684)-Net over F5 — Constructive and digital
Digital (95, 114, 8684)-net over F5, using
- 51 times duplication [i] based on digital (94, 113, 8684)-net over F5, using
- net defined by OOA [i] based on linear OOA(5113, 8684, F5, 19, 19) (dual of [(8684, 19), 164883, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(5113, 78157, F5, 19) (dual of [78157, 78044, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 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(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(5113, 78157, F5, 19) (dual of [78157, 78044, 20]-code), using
- net defined by OOA [i] based on linear OOA(5113, 8684, F5, 19, 19) (dual of [(8684, 19), 164883, 20]-NRT-code), using
(95, 114, 78162)-Net over F5 — Digital
Digital (95, 114, 78162)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5114, 78162, F5, 19) (dual of [78162, 78048, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 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(18) ⊂ Ce(13) [i] based on
- linear OA(5113, 78161, F5, 18) (dual of [78161, 78048, 19]-code), using Gilbert–Varšamov bound and bm = 5113 > Vbs−1(k−1) = 7 310659 983456 097784 627056 822724 487846 610293 560919 826415 924559 831449 062094 899905 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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
- linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code), using
- construction X with Varšamov bound [i] based on
(95, 114, large)-Net in Base 5 — Upper bound on s
There is no (95, 114, large)-net in base 5, because
- 17 times m-reduction [i] would yield (95, 97, large)-net in base 5, but