Best Known (127−28, 127, s)-Nets in Base 9
(127−28, 127, 4219)-Net over F9 — Constructive and digital
Digital (99, 127, 4219)-net over F9, using
- 92 times duplication [i] based on digital (97, 125, 4219)-net over F9, using
- net defined by OOA [i] based on linear OOA(9125, 4219, F9, 28, 28) (dual of [(4219, 28), 118007, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9125, 59066, F9, 28) (dual of [59066, 58941, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9125, 59068, F9, 28) (dual of [59068, 58943, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- 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(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(94, 19, F9, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,9)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9125, 59068, F9, 28) (dual of [59068, 58943, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9125, 59066, F9, 28) (dual of [59066, 58941, 29]-code), using
- net defined by OOA [i] based on linear OOA(9125, 4219, F9, 28, 28) (dual of [(4219, 28), 118007, 29]-NRT-code), using
(127−28, 127, 55525)-Net over F9 — Digital
Digital (99, 127, 55525)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9127, 55525, F9, 28) (dual of [55525, 55398, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9127, 59075, F9, 28) (dual of [59075, 58948, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- 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(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(96, 26, F9, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9127, 59075, F9, 28) (dual of [59075, 58948, 29]-code), using
(127−28, 127, large)-Net in Base 9 — Upper bound on s
There is no (99, 127, large)-net in base 9, because
- 26 times m-reduction [i] would yield (99, 101, large)-net in base 9, but