Best Known (40, 46, s)-Nets in Base 3
(40, 46, 59057)-Net over F3 — Constructive and digital
Digital (40, 46, 59057)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 59057, F3, 6, 6) (dual of [(59057, 6), 354296, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(346, 59057, F3, 5, 6) (dual of [(59057, 5), 295239, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(345, 177147, F3, 7) (dual of [177147, 177102, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
- appending kth column [i] based on linear OOA(346, 59057, F3, 5, 6) (dual of [(59057, 5), 295239, 7]-NRT-code), using
(40, 46, 177171)-Net over F3 — Digital
Digital (40, 46, 177171)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 177171, F3, 6, 6) (dual of [(177171, 6), 1062980, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(346, 177171, F3, 5, 6) (dual of [(177171, 5), 885809, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(345, 177147, F3, 7) (dual of [177147, 177102, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
- appending kth column [i] based on linear OOA(346, 177171, F3, 5, 6) (dual of [(177171, 5), 885809, 7]-NRT-code), using
(40, 46, large)-Net in Base 3 — Upper bound on s
There is no (40, 46, large)-net in base 3, because
- 4 times m-reduction [i] would yield (40, 42, large)-net in base 3, but