Best Known (118−21, 118, s)-Nets in Base 8
(118−21, 118, 26218)-Net over F8 — Constructive and digital
Digital (97, 118, 26218)-net over F8, using
- 82 times duplication [i] based on digital (95, 116, 26218)-net over F8, using
- net defined by OOA [i] based on linear OOA(8116, 26218, F8, 21, 21) (dual of [(26218, 21), 550462, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8116, 262181, F8, 21) (dual of [262181, 262065, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- 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(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(8116, 262181, F8, 21) (dual of [262181, 262065, 22]-code), using
- net defined by OOA [i] based on linear OOA(8116, 26218, F8, 21, 21) (dual of [(26218, 21), 550462, 22]-NRT-code), using
(118−21, 118, 262185)-Net over F8 — Digital
Digital (97, 118, 262185)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8118, 262185, F8, 21) (dual of [262185, 262067, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8116, 262181, F8, 21) (dual of [262181, 262065, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- 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(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- linear OA(8116, 262183, F8, 20) (dual of [262183, 262067, 21]-code), using Gilbert–Varšamov bound and bm = 8116 > Vbs−1(k−1) = 841286 544872 660025 493805 564257 163646 390301 630179 061239 884800 671319 606701 005079 474532 144859 955312 485092 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 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
- linear OA(8116, 262181, F8, 21) (dual of [262181, 262065, 22]-code), using
- construction X with Varšamov bound [i] based on
(118−21, 118, large)-Net in Base 8 — Upper bound on s
There is no (97, 118, large)-net in base 8, because
- 19 times m-reduction [i] would yield (97, 99, large)-net in base 8, but