Best Known (146−32, 146, s)-Nets in Base 9
(146−32, 146, 3692)-Net over F9 — Constructive and digital
Digital (114, 146, 3692)-net over F9, using
- 91 times duplication [i] based on digital (113, 145, 3692)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 3692, F9, 32, 32) (dual of [(3692, 32), 117999, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(9145, 59072, F9, 32) (dual of [59072, 58927, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(9141, 59049, F9, 32) (dual of [59049, 58908, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(9145, 59072, F9, 32) (dual of [59072, 58927, 33]-code), using
- net defined by OOA [i] based on linear OOA(9145, 3692, F9, 32, 32) (dual of [(3692, 32), 117999, 33]-NRT-code), using
(146−32, 146, 59075)-Net over F9 — Digital
Digital (114, 146, 59075)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9146, 59075, F9, 32) (dual of [59075, 58929, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(9141, 59049, F9, 32) (dual of [59049, 58908, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(9145, 59074, F9, 31) (dual of [59074, 58929, 32]-code), using Gilbert–Varšamov bound and bm = 9145 > Vbs−1(k−1) = 642006 386379 379269 871332 786891 657406 347335 024612 428974 372605 142443 517962 830969 561766 124586 958662 163695 196493 238002 334400 748535 165942 550025 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(9145, 59073, F9, 32) (dual of [59073, 58928, 33]-code), using
- construction X with Varšamov bound [i] based on
(146−32, 146, large)-Net in Base 9 — Upper bound on s
There is no (114, 146, large)-net in base 9, because
- 30 times m-reduction [i] would yield (114, 116, large)-net in base 9, but