Best Known (10, 14, s)-Nets in Base 7
(10, 14, 2403)-Net over F7 — Constructive and digital
Digital (10, 14, 2403)-net over F7, using
- net defined by OOA [i] based on linear OOA(714, 2403, F7, 4, 4) (dual of [(2403, 4), 9598, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(714, 2403, F7, 3, 4) (dual of [(2403, 3), 7195, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(714, 4806, F7, 4) (dual of [4806, 4792, 5]-code), using
- trace code [i] based on linear OA(497, 2403, F49, 4) (dual of [2403, 2396, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(497, 2401, F49, 4) (dual of [2401, 2394, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(495, 2401, F49, 3) (dual of [2401, 2396, 4]-code or 2401-cap in PG(4,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- trace code [i] based on linear OA(497, 2403, F49, 4) (dual of [2403, 2396, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(714, 4806, F7, 4) (dual of [4806, 4792, 5]-code), using
- appending kth column [i] based on linear OOA(714, 2403, F7, 3, 4) (dual of [(2403, 3), 7195, 5]-NRT-code), using
(10, 14, 4968)-Net over F7 — Digital
Digital (10, 14, 4968)-net over F7, using
- net defined by OOA [i] based on linear OOA(714, 4968, F7, 4, 4) (dual of [(4968, 4), 19858, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(714, 4968, F7, 3, 4) (dual of [(4968, 3), 14890, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(714, 4968, F7, 4) (dual of [4968, 4954, 5]-code), using
- 262 step Varšamov–Edel lengthening with (ri) = (1, 33 times 0, 1, 227 times 0) [i] based on linear OA(712, 4704, F7, 4) (dual of [4704, 4692, 5]-code), using
- trace code [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- 1 times truncation [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- trace code [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- 262 step Varšamov–Edel lengthening with (ri) = (1, 33 times 0, 1, 227 times 0) [i] based on linear OA(712, 4704, F7, 4) (dual of [4704, 4692, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(714, 4968, F7, 4) (dual of [4968, 4954, 5]-code), using
- appending kth column [i] based on linear OOA(714, 4968, F7, 3, 4) (dual of [(4968, 3), 14890, 5]-NRT-code), using
(10, 14, 194110)-Net in Base 7 — Upper bound on s
There is no (10, 14, 194111)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 678229 269109 > 714 [i]