Best Known (131−30, 131, s)-Nets in Base 9
(131−30, 131, 3936)-Net over F9 — Constructive and digital
Digital (101, 131, 3936)-net over F9, using
- net defined by OOA [i] based on linear OOA(9131, 3936, F9, 30, 30) (dual of [(3936, 30), 117949, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(9131, 59040, F9, 30) (dual of [59040, 58909, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(9131, 59040, F9, 30) (dual of [59040, 58909, 31]-code), using
(131−30, 131, 38031)-Net over F9 — Digital
Digital (101, 131, 38031)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9131, 38031, F9, 30) (dual of [38031, 37900, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
(131−30, 131, large)-Net in Base 9 — Upper bound on s
There is no (101, 131, large)-net in base 9, because
- 28 times m-reduction [i] would yield (101, 103, large)-net in base 9, but