Best Known (33, 33+7, s)-Nets in Base 5
(33, 33+7, 26069)-Net over F5 — Constructive and digital
Digital (33, 40, 26069)-net over F5, using
- net defined by OOA [i] based on linear OOA(540, 26069, F5, 9, 7) (dual of [(26069, 9), 234581, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(540, 26070, F5, 3, 7) (dual of [(26070, 3), 78170, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(54, 26, F5, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
- linear OOA(536, 26044, F5, 3, 7) (dual of [(26044, 3), 78096, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- OOA 3-folding [i] based on linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(540, 26070, F5, 3, 7) (dual of [(26070, 3), 78170, 8]-NRT-code), using
(33, 33+7, 78158)-Net over F5 — Digital
Digital (33, 40, 78158)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(540, 78158, F5, 7) (dual of [78158, 78118, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- (u, u+v)-construction [i] based on
(33, 33+7, large)-Net in Base 5 — Upper bound on s
There is no (33, 40, large)-net in base 5, because
- 5 times m-reduction [i] would yield (33, 35, large)-net in base 5, but