Best Known (68, 98, s)-Nets in Base 32
(68, 98, 2187)-Net over F32 — Constructive and digital
Digital (68, 98, 2187)-net over F32, using
- net defined by OOA [i] based on linear OOA(3298, 2187, F32, 30, 30) (dual of [(2187, 30), 65512, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3298, 32805, F32, 30) (dual of [32805, 32707, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3298, 32808, F32, 30) (dual of [32808, 32710, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(19) [i] based on
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3210, 40, F32, 9) (dual of [40, 30, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- algebraic-geometric code AG(F,33P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using
- construction X applied to Ce(29) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3298, 32808, F32, 30) (dual of [32808, 32710, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3298, 32805, F32, 30) (dual of [32805, 32707, 31]-code), using
(68, 98, 4369)-Net in Base 32 — Constructive
(68, 98, 4369)-net in base 32, using
- t-expansion [i] based on (67, 98, 4369)-net in base 32, using
- net defined by OOA [i] based on OOA(3298, 4369, S32, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(3298, 65536, S32, 31), using
- discarding factors based on OA(3298, 65538, S32, 31), using
- discarding parts of the base [i] based on linear OA(25661, 65538, F256, 31) (dual of [65538, 65477, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(25661, 65538, F256, 31) (dual of [65538, 65477, 32]-code), using
- discarding factors based on OA(3298, 65538, S32, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(3298, 65536, S32, 31), using
- net defined by OOA [i] based on OOA(3298, 4369, S32, 31, 31), using
(68, 98, 45948)-Net over F32 — Digital
Digital (68, 98, 45948)-net over F32, using
(68, 98, large)-Net in Base 32 — Upper bound on s
There is no (68, 98, large)-net in base 32, because
- 28 times m-reduction [i] would yield (68, 70, large)-net in base 32, but