Best Known (97−27, 97, s)-Nets in Base 25
(97−27, 97, 1269)-Net over F25 — Constructive and digital
Digital (70, 97, 1269)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (53, 80, 1203)-net over F25, using
- net defined by OOA [i] based on linear OOA(2580, 1203, F25, 27, 27) (dual of [(1203, 27), 32401, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2580, 15640, F25, 27) (dual of [15640, 15560, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2580, 15641, F25, 27) (dual of [15641, 15561, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(21) [i] based on
- linear OA(2576, 15625, F25, 27) (dual of [15625, 15549, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(254, 16, F25, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(26) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2580, 15641, F25, 27) (dual of [15641, 15561, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2580, 15640, F25, 27) (dual of [15640, 15560, 28]-code), using
- net defined by OOA [i] based on linear OOA(2580, 1203, F25, 27, 27) (dual of [(1203, 27), 32401, 28]-NRT-code), using
- digital (4, 17, 66)-net over F25, using
(97−27, 97, 72202)-Net over F25 — Digital
Digital (70, 97, 72202)-net over F25, using
(97−27, 97, large)-Net in Base 25 — Upper bound on s
There is no (70, 97, large)-net in base 25, because
- 25 times m-reduction [i] would yield (70, 72, large)-net in base 25, but