Best Known (93, 119, s)-Nets in Base 8
(93, 119, 2523)-Net over F8 — Constructive and digital
Digital (93, 119, 2523)-net over F8, using
- 81 times duplication [i] based on digital (92, 118, 2523)-net over F8, using
- net defined by OOA [i] based on linear OOA(8118, 2523, F8, 26, 26) (dual of [(2523, 26), 65480, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8118, 32799, F8, 26) (dual of [32799, 32681, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8118, 32799, F8, 26) (dual of [32799, 32681, 27]-code), using
- net defined by OOA [i] based on linear OOA(8118, 2523, F8, 26, 26) (dual of [(2523, 26), 65480, 27]-NRT-code), using
(93, 119, 32802)-Net over F8 — Digital
Digital (93, 119, 32802)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8119, 32802, F8, 26) (dual of [32802, 32683, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- linear OA(8118, 32801, F8, 25) (dual of [32801, 32683, 26]-code), using Gilbert–Varšamov bound and bm = 8118 > Vbs−1(k−1) = 736 223486 136599 135138 544680 368234 265794 090398 601786 440011 518989 649199 072657 334300 358692 451619 889854 230471 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X with Varšamov bound [i] based on
(93, 119, large)-Net in Base 8 — Upper bound on s
There is no (93, 119, large)-net in base 8, because
- 24 times m-reduction [i] would yield (93, 95, large)-net in base 8, but