Best Known (115, 115+26, s)-Nets in Base 8
(115, 115+26, 20167)-Net over F8 — Constructive and digital
Digital (115, 141, 20167)-net over F8, using
- 82 times duplication [i] based on digital (113, 139, 20167)-net over F8, using
- net defined by OOA [i] based on linear OOA(8139, 20167, F8, 26, 26) (dual of [(20167, 26), 524203, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8139, 262171, F8, 26) (dual of [262171, 262032, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8139, 262174, F8, 26) (dual of [262174, 262035, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(86, 30, F8, 4) (dual of [30, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8139, 262174, F8, 26) (dual of [262174, 262035, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8139, 262171, F8, 26) (dual of [262171, 262032, 27]-code), using
- net defined by OOA [i] based on linear OOA(8139, 20167, F8, 26, 26) (dual of [(20167, 26), 524203, 27]-NRT-code), using
(115, 115+26, 259577)-Net over F8 — Digital
Digital (115, 141, 259577)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8141, 259577, F8, 26) (dual of [259577, 259436, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, 262182, F8, 26) (dual of [262182, 262041, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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(25) ⊂ Ce(19) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, 262182, F8, 26) (dual of [262182, 262041, 27]-code), using
(115, 115+26, large)-Net in Base 8 — Upper bound on s
There is no (115, 141, large)-net in base 8, because
- 24 times m-reduction [i] would yield (115, 117, large)-net in base 8, but