Best Known (115, 130, s)-Nets in Base 4
(115, 130, 599196)-Net over F4 — Constructive and digital
Digital (115, 130, 599196)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (107, 122, 599187)-net over F4, using
- net defined by OOA [i] based on linear OOA(4122, 599187, F4, 15, 15) (dual of [(599187, 15), 8987683, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4122, 4194310, F4, 15) (dual of [4194310, 4194188, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4122, 4194315, F4, 15) (dual of [4194315, 4194193, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(40, 11, F4, 0) (dual of [11, 11, 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(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4122, 4194315, F4, 15) (dual of [4194315, 4194193, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4122, 4194310, F4, 15) (dual of [4194310, 4194188, 16]-code), using
- net defined by OOA [i] based on linear OOA(4122, 599187, F4, 15, 15) (dual of [(599187, 15), 8987683, 16]-NRT-code), using
- digital (1, 8, 9)-net over F4, using
(115, 130, 2097178)-Net over F4 — Digital
Digital (115, 130, 2097178)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4130, 2097178, F4, 2, 15) (dual of [(2097178, 2), 4194226, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4130, 4194356, F4, 15) (dual of [4194356, 4194226, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(4130, 4194356, F4, 15) (dual of [4194356, 4194226, 16]-code), using
(115, 130, large)-Net in Base 4 — Upper bound on s
There is no (115, 130, large)-net in base 4, because
- 13 times m-reduction [i] would yield (115, 117, large)-net in base 4, but