Best Known (37−14, 37, s)-Nets in Base 128
(37−14, 37, 2598)-Net over F128 — Constructive and digital
Digital (23, 37, 2598)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 258)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 3, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (13, 27, 2340)-net over F128, using
- net defined by OOA [i] based on linear OOA(12827, 2340, F128, 14, 14) (dual of [(2340, 14), 32733, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12827, 16380, F128, 14) (dual of [16380, 16353, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12827, 16380, F128, 14) (dual of [16380, 16353, 15]-code), using
- net defined by OOA [i] based on linear OOA(12827, 2340, F128, 14, 14) (dual of [(2340, 14), 32733, 15]-NRT-code), using
- digital (3, 10, 258)-net over F128, using
(37−14, 37, 9364)-Net in Base 128 — Constructive
(23, 37, 9364)-net in base 128, using
- 1 times m-reduction [i] based on (23, 38, 9364)-net in base 128, using
- net defined by OOA [i] based on OOA(12838, 9364, S128, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(12838, 65549, S128, 15), using
- discarding factors based on OA(12838, 65550, S128, 15), using
- discarding parts of the base [i] based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
- discarding factors based on OA(12838, 65550, S128, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(12838, 65549, S128, 15), using
- net defined by OOA [i] based on OOA(12838, 9364, S128, 15, 15), using
(37−14, 37, 44372)-Net over F128 — Digital
Digital (23, 37, 44372)-net over F128, using
(37−14, 37, large)-Net in Base 128 — Upper bound on s
There is no (23, 37, large)-net in base 128, because
- 12 times m-reduction [i] would yield (23, 25, large)-net in base 128, but