Best Known (11, 16, s)-Nets in Base 4
(11, 16, 511)-Net over F4 — Constructive and digital
Digital (11, 16, 511)-net over F4, using
- net defined by OOA [i] based on linear OOA(416, 511, F4, 5, 5) (dual of [(511, 5), 2539, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using
(11, 16, 619)-Net over F4 — Digital
Digital (11, 16, 619)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(416, 619, F4, 5) (dual of [619, 603, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using
(11, 16, 15445)-Net in Base 4 — Upper bound on s
There is no (11, 16, 15446)-net in base 4, because
- 1 times m-reduction [i] would yield (11, 15, 15446)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1073 767306 > 415 [i]