Best Known (38, 55, s)-Nets in Base 128
(38, 55, 262147)-Net over F128 — Constructive and digital
Digital (38, 55, 262147)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 262147, F128, 17, 17) (dual of [(262147, 17), 4456444, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12855, 2097177, F128, 17) (dual of [2097177, 2097122, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 2097179, F128, 17) (dual of [2097179, 2097124, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12855, 2097179, F128, 17) (dual of [2097179, 2097124, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12855, 2097177, F128, 17) (dual of [2097177, 2097122, 18]-code), using
(38, 55, 1949474)-Net over F128 — Digital
Digital (38, 55, 1949474)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12855, 1949474, F128, 17) (dual of [1949474, 1949419, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 2097179, F128, 17) (dual of [2097179, 2097124, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12855, 2097179, F128, 17) (dual of [2097179, 2097124, 18]-code), using
(38, 55, large)-Net in Base 128 — Upper bound on s
There is no (38, 55, large)-net in base 128, because
- 15 times m-reduction [i] would yield (38, 40, large)-net in base 128, but