Best Known (146−33, 146, s)-Nets in Base 8
(146−33, 146, 2049)-Net over F8 — Constructive and digital
Digital (113, 146, 2049)-net over F8, using
- 81 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
(146−33, 146, 29702)-Net over F8 — Digital
Digital (113, 146, 29702)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8146, 29702, F8, 33) (dual of [29702, 29556, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 32789, F8, 33) (dual of [32789, 32643, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(28) ⊂ Ce(27) [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(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(84, 20, F8, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,8)), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(32) ⊂ Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8146, 32789, F8, 33) (dual of [32789, 32643, 34]-code), using
(146−33, 146, large)-Net in Base 8 — Upper bound on s
There is no (113, 146, large)-net in base 8, because
- 31 times m-reduction [i] would yield (113, 115, large)-net in base 8, but