Best Known (140−20, 140, s)-Nets in Base 4
(140−20, 140, 26217)-Net over F4 — Constructive and digital
Digital (120, 140, 26217)-net over F4, using
- net defined by OOA [i] based on linear OOA(4140, 26217, F4, 20, 20) (dual of [(26217, 20), 524200, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4140, 262170, F4, 20) (dual of [262170, 262030, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 262175, F4, 20) (dual of [262175, 262035, 21]-code), using
- 1 times truncation [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-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(20) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 262175, F4, 20) (dual of [262175, 262035, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4140, 262170, F4, 20) (dual of [262170, 262030, 21]-code), using
(140−20, 140, 131087)-Net over F4 — Digital
Digital (120, 140, 131087)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4140, 131087, F4, 2, 20) (dual of [(131087, 2), 262034, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4140, 262174, F4, 20) (dual of [262174, 262034, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 262175, F4, 20) (dual of [262175, 262035, 21]-code), using
- 1 times truncation [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-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(20) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 262175, F4, 20) (dual of [262175, 262035, 21]-code), using
- OOA 2-folding [i] based on linear OA(4140, 262174, F4, 20) (dual of [262174, 262034, 21]-code), using
(140−20, 140, large)-Net in Base 4 — Upper bound on s
There is no (120, 140, large)-net in base 4, because
- 18 times m-reduction [i] would yield (120, 122, large)-net in base 4, but