Best Known (93, 109, s)-Nets in Base 7
(93, 109, 720603)-Net over F7 — Constructive and digital
Digital (93, 109, 720603)-net over F7, using
- net defined by OOA [i] based on linear OOA(7109, 720603, F7, 16, 16) (dual of [(720603, 16), 11529539, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(7109, 5764824, F7, 16) (dual of [5764824, 5764715, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(7109, 5764829, F7, 16) (dual of [5764829, 5764720, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(7109, 5764829, F7, 16) (dual of [5764829, 5764720, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(7109, 5764824, F7, 16) (dual of [5764824, 5764715, 17]-code), using
(93, 109, 3331449)-Net over F7 — Digital
Digital (93, 109, 3331449)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7109, 3331449, F7, 16) (dual of [3331449, 3331340, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(7109, 5764829, F7, 16) (dual of [5764829, 5764720, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(7109, 5764829, F7, 16) (dual of [5764829, 5764720, 17]-code), using
(93, 109, large)-Net in Base 7 — Upper bound on s
There is no (93, 109, large)-net in base 7, because
- 14 times m-reduction [i] would yield (93, 95, large)-net in base 7, but