Best Known (104−20, 104, s)-Nets in Base 8
(104−20, 104, 26215)-Net over F8 — Constructive and digital
Digital (84, 104, 26215)-net over F8, using
- 81 times duplication [i] based on digital (83, 103, 26215)-net over F8, using
- net defined by OOA [i] based on linear OOA(8103, 26215, F8, 20, 20) (dual of [(26215, 20), 524197, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8103, 262150, F8, 20) (dual of [262150, 262047, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- 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(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 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
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- OA 10-folding and stacking [i] based on linear OA(8103, 262150, F8, 20) (dual of [262150, 262047, 21]-code), using
- net defined by OOA [i] based on linear OOA(8103, 26215, F8, 20, 20) (dual of [(26215, 20), 524197, 21]-NRT-code), using
(104−20, 104, 158739)-Net over F8 — Digital
Digital (84, 104, 158739)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8104, 158739, F8, 20) (dual of [158739, 158635, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8104, 262157, F8, 20) (dual of [262157, 262053, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- 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(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 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
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8104, 262157, F8, 20) (dual of [262157, 262053, 21]-code), using
(104−20, 104, large)-Net in Base 8 — Upper bound on s
There is no (84, 104, large)-net in base 8, because
- 18 times m-reduction [i] would yield (84, 86, large)-net in base 8, but