Best Known (102, 102+24, s)-Nets in Base 4
(102, 102+24, 1365)-Net over F4 — Constructive and digital
Digital (102, 126, 1365)-net over F4, using
- net defined by OOA [i] based on linear OOA(4126, 1365, F4, 24, 24) (dual of [(1365, 24), 32634, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4126, 16380, F4, 24) (dual of [16380, 16254, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 16384, F4, 24) (dual of [16384, 16258, 25]-code), using
- 1 times truncation [i] based on linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 16384, F4, 24) (dual of [16384, 16258, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4126, 16380, F4, 24) (dual of [16380, 16254, 25]-code), using
(102, 102+24, 8192)-Net over F4 — Digital
Digital (102, 126, 8192)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4126, 8192, F4, 2, 24) (dual of [(8192, 2), 16258, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4126, 16384, F4, 24) (dual of [16384, 16258, 25]-code), using
- 1 times truncation [i] based on linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using
- OOA 2-folding [i] based on linear OA(4126, 16384, F4, 24) (dual of [16384, 16258, 25]-code), using
(102, 102+24, 3697166)-Net in Base 4 — Upper bound on s
There is no (102, 126, 3697167)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7237 028775 676985 181672 985334 339390 079761 197604 567488 780526 016319 764241 918795 > 4126 [i]