Best Known (97−16, 97, s)-Nets in Base 8
(97−16, 97, 65538)-Net over F8 — Constructive and digital
Digital (81, 97, 65538)-net over F8, using
- 81 times duplication [i] based on digital (80, 96, 65538)-net over F8, using
- net defined by OOA [i] based on linear OOA(896, 65538, F8, 16, 16) (dual of [(65538, 16), 1048512, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(896, 524304, F8, 16) (dual of [524304, 524208, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(896, 524310, F8, 16) (dual of [524310, 524214, 17]-code), using
- trace code [i] based on linear OA(6448, 262155, F64, 16) (dual of [262155, 262107, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(15) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(6448, 262155, F64, 16) (dual of [262155, 262107, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(896, 524310, F8, 16) (dual of [524310, 524214, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(896, 524304, F8, 16) (dual of [524304, 524208, 17]-code), using
- net defined by OOA [i] based on linear OOA(896, 65538, F8, 16, 16) (dual of [(65538, 16), 1048512, 17]-NRT-code), using
(97−16, 97, 634827)-Net over F8 — Digital
Digital (81, 97, 634827)-net over F8, using
(97−16, 97, large)-Net in Base 8 — Upper bound on s
There is no (81, 97, large)-net in base 8, because
- 14 times m-reduction [i] would yield (81, 83, large)-net in base 8, but