Best Known (24, 24+18, s)-Nets in Base 128
(24, 24+18, 1823)-Net over F128 — Constructive and digital
Digital (24, 42, 1823)-net over F128, using
- net defined by OOA [i] based on linear OOA(12842, 1823, F128, 18, 18) (dual of [(1823, 18), 32772, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12842, 16407, F128, 18) (dual of [16407, 16365, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(9) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(17) ⊂ Ce(9) [i] based on
- OA 9-folding and stacking [i] based on linear OA(12842, 16407, F128, 18) (dual of [16407, 16365, 19]-code), using
(24, 24+18, 7282)-Net in Base 128 — Constructive
(24, 42, 7282)-net in base 128, using
- 1282 times duplication [i] based on (22, 40, 7282)-net in base 128, using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
(24, 24+18, 13435)-Net over F128 — Digital
Digital (24, 42, 13435)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12842, 13435, F128, 18) (dual of [13435, 13393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12842, 16407, F128, 18) (dual of [16407, 16365, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(9) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(17) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12842, 16407, F128, 18) (dual of [16407, 16365, 19]-code), using
(24, 24+18, large)-Net in Base 128 — Upper bound on s
There is no (24, 42, large)-net in base 128, because
- 16 times m-reduction [i] would yield (24, 26, large)-net in base 128, but