Best Known (103, 103+22, s)-Nets in Base 5
(103, 103+22, 7104)-Net over F5 — Constructive and digital
Digital (103, 125, 7104)-net over F5, using
- 51 times duplication [i] based on digital (102, 124, 7104)-net over F5, using
- net defined by OOA [i] based on linear OOA(5124, 7104, F5, 22, 22) (dual of [(7104, 22), 156164, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5124, 78144, F5, 22) (dual of [78144, 78020, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5124, 78150, F5, 22) (dual of [78150, 78026, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5124, 78150, F5, 22) (dual of [78150, 78026, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(5124, 78144, F5, 22) (dual of [78144, 78020, 23]-code), using
- net defined by OOA [i] based on linear OOA(5124, 7104, F5, 22, 22) (dual of [(7104, 22), 156164, 23]-NRT-code), using
(103, 103+22, 44743)-Net over F5 — Digital
Digital (103, 125, 44743)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5125, 44743, F5, 22) (dual of [44743, 44618, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5125, 78152, F5, 22) (dual of [78152, 78027, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5125, 78152, F5, 22) (dual of [78152, 78027, 23]-code), using
(103, 103+22, large)-Net in Base 5 — Upper bound on s
There is no (103, 125, large)-net in base 5, because
- 20 times m-reduction [i] would yield (103, 105, large)-net in base 5, but