Best Known (37, 76, s)-Nets in Base 27
(37, 76, 178)-Net over F27 — Constructive and digital
Digital (37, 76, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 27, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 49, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (8, 27, 84)-net over F27, using
(37, 76, 370)-Net in Base 27 — Constructive
(37, 76, 370)-net in base 27, using
- 8 times m-reduction [i] based on (37, 84, 370)-net in base 27, using
- base change [i] based on digital (16, 63, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 63, 370)-net over F81, using
(37, 76, 433)-Net over F27 — Digital
Digital (37, 76, 433)-net over F27, using
(37, 76, 136248)-Net in Base 27 — Upper bound on s
There is no (37, 76, 136249)-net in base 27, because
- 1 times m-reduction [i] would yield (37, 75, 136249)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 225071 977092 465238 623223 131866 639432 917731 605912 320841 271626 919350 541535 111800 580297 181731 475161 252064 517507 > 2775 [i]