Best Known (91−15, 91, s)-Nets in Base 8
(91−15, 91, 74901)-Net over F8 — Constructive and digital
Digital (76, 91, 74901)-net over F8, using
- 81 times duplication [i] based on digital (75, 90, 74901)-net over F8, using
- net defined by OOA [i] based on linear OOA(890, 74901, F8, 15, 15) (dual of [(74901, 15), 1123425, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(890, 524308, F8, 15) (dual of [524308, 524218, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(890, 524310, F8, 15) (dual of [524310, 524220, 16]-code), using
- trace code [i] based on linear OA(6445, 262155, F64, 15) (dual of [262155, 262110, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(11) [i] based on
- linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-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(14) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(6445, 262155, F64, 15) (dual of [262155, 262110, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(890, 524310, F8, 15) (dual of [524310, 524220, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(890, 524308, F8, 15) (dual of [524308, 524218, 16]-code), using
- net defined by OOA [i] based on linear OOA(890, 74901, F8, 15, 15) (dual of [(74901, 15), 1123425, 16]-NRT-code), using
(91−15, 91, 640397)-Net over F8 — Digital
Digital (76, 91, 640397)-net over F8, using
(91−15, 91, large)-Net in Base 8 — Upper bound on s
There is no (76, 91, large)-net in base 8, because
- 13 times m-reduction [i] would yield (76, 78, large)-net in base 8, but