Best Known (116, 116+26, s)-Nets in Base 8
(116, 116+26, 20167)-Net over F8 — Constructive and digital
Digital (116, 142, 20167)-net over F8, using
- 83 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
(116, 116+26, 262184)-Net over F8 — Digital
Digital (116, 142, 262184)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8142, 262184, F8, 26) (dual of [262184, 262042, 27]-code), using
- construction X with Varšamov bound [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
- linear OA(8140, 262182, F8, 24) (dual of [262182, 262042, 25]-code), using Gilbert–Varšamov bound and bm = 8140 > Vbs−1(k−1) = 44 892603 789316 089569 088653 481570 084917 649643 136163 701904 756468 834255 430563 880674 177276 023366 324579 938010 837769 807032 269664 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- construction X with Varšamov bound [i] based on
(116, 116+26, large)-Net in Base 8 — Upper bound on s
There is no (116, 142, large)-net in base 8, because
- 24 times m-reduction [i] would yield (116, 118, large)-net in base 8, but