Best Known (200, 200+33, s)-Nets in Base 4
(200, 200+33, 16389)-Net over F4 — Constructive and digital
Digital (200, 233, 16389)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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 (184, 217, 16384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- digital (0, 16, 5)-net over F4, using
(200, 200+33, 132608)-Net over F4 — Digital
Digital (200, 233, 132608)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4233, 132608, F4, 33) (dual of [132608, 132375, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4233, 262162, F4, 33) (dual of [262162, 261929, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([1,16]) [i] based on
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4216, 262145, F4, 16) (dual of [262145, 261929, 17]-code), using the narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(416, 17, F4, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,4)), using
- dual of repetition code with length 17 [i]
- construction X applied to C([0,16]) ⊂ C([1,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4233, 262162, F4, 33) (dual of [262162, 261929, 34]-code), using
(200, 200+33, large)-Net in Base 4 — Upper bound on s
There is no (200, 233, large)-net in base 4, because
- 31 times m-reduction [i] would yield (200, 202, large)-net in base 4, but