Best Known (110, 133, s)-Nets in Base 5
(110, 133, 7104)-Net over F5 — Constructive and digital
Digital (110, 133, 7104)-net over F5, using
- 52 times duplication [i] based on digital (108, 131, 7104)-net over F5, using
- net defined by OOA [i] based on linear OOA(5131, 7104, F5, 23, 23) (dual of [(7104, 23), 163261, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5131, 78145, F5, 23) (dual of [78145, 78014, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5131, 78150, F5, 23) (dual of [78150, 78019, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5131, 78150, F5, 23) (dual of [78150, 78019, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5131, 78145, F5, 23) (dual of [78145, 78014, 24]-code), using
- net defined by OOA [i] based on linear OOA(5131, 7104, F5, 23, 23) (dual of [(7104, 23), 163261, 24]-NRT-code), using
(110, 133, 53683)-Net over F5 — Digital
Digital (110, 133, 53683)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5133, 53683, F5, 23) (dual of [53683, 53550, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5133, 78155, F5, 23) (dual of [78155, 78022, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5133, 78155, F5, 23) (dual of [78155, 78022, 24]-code), using
(110, 133, large)-Net in Base 5 — Upper bound on s
There is no (110, 133, large)-net in base 5, because
- 21 times m-reduction [i] would yield (110, 112, large)-net in base 5, but