Best Known (76, 93, s)-Nets in Base 4
(76, 93, 2053)-Net over F4 — Constructive and digital
Digital (76, 93, 2053)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (68, 85, 2048)-net over F4, using
- net defined by OOA [i] based on linear OOA(485, 2048, F4, 17, 17) (dual of [(2048, 17), 34731, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using
- net defined by OOA [i] based on linear OOA(485, 2048, F4, 17, 17) (dual of [(2048, 17), 34731, 18]-NRT-code), using
- digital (0, 8, 5)-net over F4, using
(76, 93, 10539)-Net over F4 — Digital
Digital (76, 93, 10539)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(493, 10539, F4, 17) (dual of [10539, 10446, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(493, 16394, F4, 17) (dual of [16394, 16301, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([1,8]) [i] based on
- linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(484, 16385, F4, 8) (dual of [16385, 16301, 9]-code), using the narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- construction X applied to C([0,8]) ⊂ C([1,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(493, 16394, F4, 17) (dual of [16394, 16301, 18]-code), using
(76, 93, large)-Net in Base 4 — Upper bound on s
There is no (76, 93, large)-net in base 4, because
- 15 times m-reduction [i] would yield (76, 78, large)-net in base 4, but