Best Known (237−104, 237, s)-Nets in Base 4
(237−104, 237, 130)-Net over F4 — Constructive and digital
Digital (133, 237, 130)-net over F4, using
- t-expansion [i] based on digital (105, 237, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(237−104, 237, 252)-Net over F4 — Digital
Digital (133, 237, 252)-net over F4, using
(237−104, 237, 3696)-Net in Base 4 — Upper bound on s
There is no (133, 237, 3697)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 49073 522891 255014 780834 196736 509111 655180 008947 322929 453514 458650 742938 282324 946028 177047 922469 034239 436915 660297 703496 332440 448486 562100 251280 > 4237 [i]