Best Known (93−16, 93, s)-Nets in Base 7
(93−16, 93, 102943)-Net over F7 — Constructive and digital
Digital (77, 93, 102943)-net over F7, using
- 71 times duplication [i] based on digital (76, 92, 102943)-net over F7, using
- net defined by OOA [i] based on linear OOA(792, 102943, F7, 16, 16) (dual of [(102943, 16), 1646996, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(792, 823544, F7, 16) (dual of [823544, 823452, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 823550, F7, 16) (dual of [823550, 823458, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [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(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 823550, F7, 16) (dual of [823550, 823458, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(792, 823544, F7, 16) (dual of [823544, 823452, 17]-code), using
- net defined by OOA [i] based on linear OOA(792, 102943, F7, 16, 16) (dual of [(102943, 16), 1646996, 17]-NRT-code), using
(93−16, 93, 411775)-Net over F7 — Digital
Digital (77, 93, 411775)-net over F7, using
- 71 times duplication [i] based on digital (76, 92, 411775)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(792, 411775, F7, 2, 16) (dual of [(411775, 2), 823458, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(792, 823550, F7, 16) (dual of [823550, 823458, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [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(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(792, 823550, F7, 16) (dual of [823550, 823458, 17]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(792, 411775, F7, 2, 16) (dual of [(411775, 2), 823458, 17]-NRT-code), using
(93−16, 93, large)-Net in Base 7 — Upper bound on s
There is no (77, 93, large)-net in base 7, because
- 14 times m-reduction [i] would yield (77, 79, large)-net in base 7, but