Best Known (121−23, 121, s)-Nets in Base 8
(121−23, 121, 23831)-Net over F8 — Constructive and digital
Digital (98, 121, 23831)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 23831, F8, 23, 23) (dual of [(23831, 23), 547992, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8121, 262142, F8, 23) (dual of [262142, 262021, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8121, 262142, F8, 23) (dual of [262142, 262021, 24]-code), using
(121−23, 121, 179423)-Net over F8 — Digital
Digital (98, 121, 179423)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8121, 179423, F8, 23) (dual of [179423, 179302, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using
(121−23, 121, large)-Net in Base 8 — Upper bound on s
There is no (98, 121, large)-net in base 8, because
- 21 times m-reduction [i] would yield (98, 100, large)-net in base 8, but