Best Known (59, 59+12, s)-Nets in Base 8
(59, 59+12, 349526)-Net over F8 — Constructive and digital
Digital (59, 71, 349526)-net over F8, using
- net defined by OOA [i] based on linear OOA(871, 349526, F8, 12, 12) (dual of [(349526, 12), 4194241, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(871, 2097156, F8, 12) (dual of [2097156, 2097085, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(871, 2097159, F8, 12) (dual of [2097159, 2097088, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(871, 2097159, F8, 12) (dual of [2097159, 2097088, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(871, 2097156, F8, 12) (dual of [2097156, 2097085, 13]-code), using
(59, 59+12, 1356771)-Net over F8 — Digital
Digital (59, 71, 1356771)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(871, 1356771, F8, 12) (dual of [1356771, 1356700, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using
(59, 59+12, large)-Net in Base 8 — Upper bound on s
There is no (59, 71, large)-net in base 8, because
- 10 times m-reduction [i] would yield (59, 61, large)-net in base 8, but