Best Known (107, 133, s)-Nets in Base 5
(107, 133, 1205)-Net over F5 — Constructive and digital
Digital (107, 133, 1205)-net over F5, using
- 51 times duplication [i] based on digital (106, 132, 1205)-net over F5, using
- net defined by OOA [i] based on linear OOA(5132, 1205, F5, 26, 26) (dual of [(1205, 26), 31198, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5132, 15665, F5, 26) (dual of [15665, 15533, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(511, 41, F5, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5132, 15665, F5, 26) (dual of [15665, 15533, 27]-code), using
- net defined by OOA [i] based on linear OOA(5132, 1205, F5, 26, 26) (dual of [(1205, 26), 31198, 27]-NRT-code), using
(107, 133, 15668)-Net over F5 — Digital
Digital (107, 133, 15668)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5133, 15668, F5, 26) (dual of [15668, 15535, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(511, 41, F5, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5132, 15667, F5, 25) (dual of [15667, 15535, 26]-code), using Gilbert–Varšamov bound and bm = 5132 > Vbs−1(k−1) = 21 293180 311685 712803 064454 048192 302319 867589 369071 916419 952181 467936 866176 086350 305725 716825 [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(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using
- construction X with Varšamov bound [i] based on
(107, 133, large)-Net in Base 5 — Upper bound on s
There is no (107, 133, large)-net in base 5, because
- 24 times m-reduction [i] would yield (107, 109, large)-net in base 5, but