Best Known (200−30, 200, s)-Nets in Base 3
(200−30, 200, 3936)-Net over F3 — Constructive and digital
Digital (170, 200, 3936)-net over F3, using
- net defined by OOA [i] based on linear OOA(3200, 3936, F3, 30, 30) (dual of [(3936, 30), 117880, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3200, 59040, F3, 30) (dual of [59040, 58840, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3200, 59049, F3, 30) (dual of [59049, 58849, 31]-code), using
- 1 times truncation [i] based on linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3200, 59049, F3, 30) (dual of [59049, 58849, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3200, 59040, F3, 30) (dual of [59040, 58840, 31]-code), using
(200−30, 200, 19683)-Net over F3 — Digital
Digital (170, 200, 19683)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3200, 19683, F3, 3, 30) (dual of [(19683, 3), 58849, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3200, 59049, F3, 30) (dual of [59049, 58849, 31]-code), using
- 1 times truncation [i] based on linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using
- OOA 3-folding [i] based on linear OA(3200, 59049, F3, 30) (dual of [59049, 58849, 31]-code), using
(200−30, 200, 7385034)-Net in Base 3 — Upper bound on s
There is no (170, 200, 7385035)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 265614 318616 692207 798476 519724 373499 417086 110234 958837 979454 900118 629105 387945 850523 526386 988051 > 3200 [i]