Best Known (94, 94+14, s)-Nets in Base 5
(94, 94+14, 279029)-Net over F5 — Constructive and digital
Digital (94, 108, 279029)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (86, 100, 279019)-net over F5, using
- net defined by OOA [i] based on linear OOA(5100, 279019, F5, 14, 14) (dual of [(279019, 14), 3906166, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(5100, 1953133, F5, 14) (dual of [1953133, 1953033, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 1953134, F5, 14) (dual of [1953134, 1953034, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(50, 9, F5, 0) (dual of [9, 9, 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 X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(5100, 1953134, F5, 14) (dual of [1953134, 1953034, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(5100, 1953133, F5, 14) (dual of [1953133, 1953033, 15]-code), using
- net defined by OOA [i] based on linear OOA(5100, 279019, F5, 14, 14) (dual of [(279019, 14), 3906166, 15]-NRT-code), using
- digital (1, 8, 10)-net over F5, using
(94, 94+14, 1953170)-Net over F5 — Digital
Digital (94, 108, 1953170)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5108, 1953170, F5, 14) (dual of [1953170, 1953062, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5107, 1953168, F5, 14) (dual of [1953168, 1953061, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(57, 43, F5, 4) (dual of [43, 36, 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(13) ⊂ Ce(8) [i] based on
- linear OA(5107, 1953169, F5, 13) (dual of [1953169, 1953062, 14]-code), using Gilbert–Varšamov bound and bm = 5107 > Vbs−1(k−1) = 107 955339 541219 466852 100040 116705 258609 163895 280716 929865 106896 802259 564993 [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(5107, 1953168, F5, 14) (dual of [1953168, 1953061, 15]-code), using
- construction X with Varšamov bound [i] based on
(94, 94+14, large)-Net in Base 5 — Upper bound on s
There is no (94, 108, large)-net in base 5, because
- 12 times m-reduction [i] would yield (94, 96, large)-net in base 5, but