Best Known (207, 247, s)-Nets in Base 4
(207, 247, 3278)-Net over F4 — Constructive and digital
Digital (207, 247, 3278)-net over F4, using
- 41 times duplication [i] based on digital (206, 246, 3278)-net over F4, using
- t-expansion [i] based on digital (205, 246, 3278)-net over F4, using
- net defined by OOA [i] based on linear OOA(4246, 3278, F4, 41, 41) (dual of [(3278, 41), 134152, 42]-NRT-code), using
- OOA 20-folding and stacking with additional row [i] based on linear OA(4246, 65561, F4, 41) (dual of [65561, 65315, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 65565, F4, 41) (dual of [65565, 65319, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(4246, 65565, F4, 41) (dual of [65565, 65319, 42]-code), using
- OOA 20-folding and stacking with additional row [i] based on linear OA(4246, 65561, F4, 41) (dual of [65561, 65315, 42]-code), using
- net defined by OOA [i] based on linear OOA(4246, 3278, F4, 41, 41) (dual of [(3278, 41), 134152, 42]-NRT-code), using
- t-expansion [i] based on digital (205, 246, 3278)-net over F4, using
(207, 247, 39527)-Net over F4 — Digital
Digital (207, 247, 39527)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4247, 39527, F4, 40) (dual of [39527, 39280, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4247, 65567, F4, 40) (dual of [65567, 65320, 41]-code), using
- 1 times truncation [i] based on linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code), using
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4247, 65567, F4, 40) (dual of [65567, 65320, 41]-code), using
(207, 247, large)-Net in Base 4 — Upper bound on s
There is no (207, 247, large)-net in base 4, because
- 38 times m-reduction [i] would yield (207, 209, large)-net in base 4, but