Best Known (30, 30+13, s)-Nets in Base 25
(30, 30+13, 2630)-Net over F25 — Constructive and digital
Digital (30, 43, 2630)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (24, 37, 2604)-net over F25, using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- digital (0, 6, 26)-net over F25, using
(30, 30+13, 22519)-Net over F25 — Digital
Digital (30, 43, 22519)-net over F25, using
(30, 30+13, large)-Net in Base 25 — Upper bound on s
There is no (30, 43, large)-net in base 25, because
- 11 times m-reduction [i] would yield (30, 32, large)-net in base 25, but