Best Known (50−12, 50, s)-Nets in Base 8
(50−12, 50, 1368)-Net over F8 — Constructive and digital
Digital (38, 50, 1368)-net over F8, using
- net defined by OOA [i] based on linear OOA(850, 1368, F8, 12, 12) (dual of [(1368, 12), 16366, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(850, 8208, F8, 12) (dual of [8208, 8158, 13]-code), using
- trace code [i] based on linear OA(6425, 4104, F64, 12) (dual of [4104, 4079, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6417, 4096, F64, 9) (dual of [4096, 4079, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- trace code [i] based on linear OA(6425, 4104, F64, 12) (dual of [4104, 4079, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(850, 8208, F8, 12) (dual of [8208, 8158, 13]-code), using
(50−12, 50, 8936)-Net over F8 — Digital
Digital (38, 50, 8936)-net over F8, using
(50−12, 50, large)-Net in Base 8 — Upper bound on s
There is no (38, 50, large)-net in base 8, because
- 10 times m-reduction [i] would yield (38, 40, large)-net in base 8, but