Best Known (115, 115+33, s)-Nets in Base 8
(115, 115+33, 2049)-Net over F8 — Constructive and digital
Digital (115, 148, 2049)-net over F8, using
- 83 times duplication [i] based on digital (112, 145, 2049)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 2049, F8, 33, 33) (dual of [(2049, 33), 67472, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8145, 32785, F8, 33) (dual of [32785, 32640, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 32787, F8, 33) (dual of [32787, 32642, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 32787, F8, 33) (dual of [32787, 32642, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8145, 32785, F8, 33) (dual of [32785, 32640, 34]-code), using
- net defined by OOA [i] based on linear OOA(8145, 2049, F8, 33, 33) (dual of [(2049, 33), 67472, 34]-NRT-code), using
(115, 115+33, 32800)-Net over F8 — Digital
Digital (115, 148, 32800)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
(115, 115+33, large)-Net in Base 8 — Upper bound on s
There is no (115, 148, large)-net in base 8, because
- 31 times m-reduction [i] would yield (115, 117, large)-net in base 8, but