Best Known (20, 32, s)-Nets in Base 128
(20, 32, 2989)-Net over F128 — Constructive and digital
Digital (20, 32, 2989)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 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, 6, 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 (11, 23, 2731)-net over F128, using
- net defined by OOA [i] based on linear OOA(12823, 2731, F128, 12, 12) (dual of [(2731, 12), 32749, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- net defined by OOA [i] based on linear OOA(12823, 2731, F128, 12, 12) (dual of [(2731, 12), 32749, 13]-NRT-code), using
- digital (3, 9, 258)-net over F128, using
(20, 32, 10925)-Net in Base 128 — Constructive
(20, 32, 10925)-net in base 128, using
- base change [i] based on digital (16, 28, 10925)-net over F256, using
- 2561 times duplication [i] based on digital (15, 27, 10925)-net over F256, using
- net defined by OOA [i] based on linear OOA(25627, 10925, F256, 12, 12) (dual of [(10925, 12), 131073, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25627, 65550, F256, 12) (dual of [65550, 65523, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(11) ⊂ Ce(6) [i] based on
- OA 6-folding and stacking [i] based on linear OA(25627, 65550, F256, 12) (dual of [65550, 65523, 13]-code), using
- net defined by OOA [i] based on linear OOA(25627, 10925, F256, 12, 12) (dual of [(10925, 12), 131073, 13]-NRT-code), using
- 2561 times duplication [i] based on digital (15, 27, 10925)-net over F256, using
(20, 32, 52158)-Net over F128 — Digital
Digital (20, 32, 52158)-net over F128, using
(20, 32, 56449)-Net in Base 128
(20, 32, 56449)-net in base 128, using
- base change [i] based on digital (16, 28, 56449)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25628, 56449, F256, 12) (dual of [56449, 56421, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, 65553, F256, 12) (dual of [65553, 65525, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(5) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to Ce(11) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(25628, 65553, F256, 12) (dual of [65553, 65525, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25628, 56449, F256, 12) (dual of [56449, 56421, 13]-code), using
(20, 32, large)-Net in Base 128 — Upper bound on s
There is no (20, 32, large)-net in base 128, because
- 10 times m-reduction [i] would yield (20, 22, large)-net in base 128, but