Best Known (99, 99+22, s)-Nets in Base 5
(99, 99+22, 7103)-Net over F5 — Constructive and digital
Digital (99, 121, 7103)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 7103, F5, 22, 22) (dual of [(7103, 22), 156145, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5121, 78133, F5, 22) (dual of [78133, 78012, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5120, 78132, F5, 22) (dual of [78132, 78012, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [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(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 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(21) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5120, 78132, F5, 22) (dual of [78132, 78012, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(5121, 78133, F5, 22) (dual of [78133, 78012, 23]-code), using
(99, 99+22, 39066)-Net over F5 — Digital
Digital (99, 121, 39066)-net over F5, using
- 51 times duplication [i] based on digital (98, 120, 39066)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5120, 39066, F5, 2, 22) (dual of [(39066, 2), 78012, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5120, 78132, F5, 22) (dual of [78132, 78012, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [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(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 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(21) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(5120, 78132, F5, 22) (dual of [78132, 78012, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5120, 39066, F5, 2, 22) (dual of [(39066, 2), 78012, 23]-NRT-code), using
(99, 99+22, large)-Net in Base 5 — Upper bound on s
There is no (99, 121, large)-net in base 5, because
- 20 times m-reduction [i] would yield (99, 101, large)-net in base 5, but