Best Known (84, 84+14, s)-Nets in Base 2
(84, 84+14, 2340)-Net over F2 — Constructive and digital
Digital (84, 98, 2340)-net over F2, using
- net defined by OOA [i] based on linear OOA(298, 2340, F2, 14, 14) (dual of [(2340, 14), 32662, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(298, 16380, F2, 14) (dual of [16380, 16282, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 16383, F2, 14) (dual of [16383, 16285, 15]-code), using
- 1 times truncation [i] based on linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 16383, F2, 14) (dual of [16383, 16285, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(298, 16380, F2, 14) (dual of [16380, 16282, 15]-code), using
(84, 84+14, 4095)-Net over F2 — Digital
Digital (84, 98, 4095)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(298, 4095, F2, 4, 14) (dual of [(4095, 4), 16282, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(298, 16380, F2, 14) (dual of [16380, 16282, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 16383, F2, 14) (dual of [16383, 16285, 15]-code), using
- 1 times truncation [i] based on linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 16383, F2, 14) (dual of [16383, 16285, 15]-code), using
- OOA 4-folding [i] based on linear OA(298, 16380, F2, 14) (dual of [16380, 16282, 15]-code), using
(84, 84+14, 55368)-Net in Base 2 — Upper bound on s
There is no (84, 98, 55369)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 316945 934018 994744 324171 457280 > 298 [i]