Best Known (98−16, 98, s)-Nets in Base 7
(98−16, 98, 102947)-Net over F7 — Constructive and digital
Digital (82, 98, 102947)-net over F7, using
- net defined by OOA [i] based on linear OOA(798, 102947, F7, 16, 16) (dual of [(102947, 16), 1647054, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(798, 823576, F7, 16) (dual of [823576, 823478, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(798, 823577, F7, 16) (dual of [823577, 823479, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(76, 34, F7, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(798, 823577, F7, 16) (dual of [823577, 823479, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(798, 823576, F7, 16) (dual of [823576, 823478, 17]-code), using
(98−16, 98, 722144)-Net over F7 — Digital
Digital (82, 98, 722144)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(798, 722144, F7, 16) (dual of [722144, 722046, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(798, 823577, F7, 16) (dual of [823577, 823479, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(76, 34, F7, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(798, 823577, F7, 16) (dual of [823577, 823479, 17]-code), using
(98−16, 98, large)-Net in Base 7 — Upper bound on s
There is no (82, 98, large)-net in base 7, because
- 14 times m-reduction [i] would yield (82, 84, large)-net in base 7, but