Best Known (43, 50, s)-Nets in Base 4
(43, 50, 87401)-Net over F4 — Constructive and digital
Digital (43, 50, 87401)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 17)-net over F4, using
- net defined by OOA [i] based on linear OOA(44, 17, F4, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- digital (39, 46, 87384)-net over F4, using
- net defined by OOA [i] based on linear OOA(446, 87384, F4, 7, 7) (dual of [(87384, 7), 611642, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(446, 262153, F4, 7) (dual of [262153, 262107, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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 and stacking with additional row [i] based on linear OA(446, 262153, F4, 7) (dual of [262153, 262107, 8]-code), using
- net defined by OOA [i] based on linear OOA(446, 87384, F4, 7, 7) (dual of [(87384, 7), 611642, 8]-NRT-code), using
- digital (1, 4, 17)-net over F4, using
(43, 50, 262170)-Net over F4 — Digital
Digital (43, 50, 262170)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(450, 262170, F4, 7) (dual of [262170, 262120, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(446, 262153, F4, 7) (dual of [262153, 262107, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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
(43, 50, large)-Net in Base 4 — Upper bound on s
There is no (43, 50, large)-net in base 4, because
- 5 times m-reduction [i] would yield (43, 45, large)-net in base 4, but