MinT - Best Known (234−105, 234, s)-Nets in Base 4

Best Known (234−105, 234, s)-Nets in Base 4

(234−105, 234, 130)-Net over F₄ — Constructive and digital

Digital (129, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(234−105, 234, 232)-Net over F₄ — Digital

Digital (129, 234, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−105, 234, 3318)-Net in Base 4 — Upper bound on s

There is no (129, 234, 3319)-net in base 4, because

1 times m-reduction [i] would yield (129, 233, 3319)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 192 408832 318853 033319 057542 590243 824483 984107 388047 423811 164642 699718 210752 957302 264666 679081 974928 775599 733390 411279 521604 058947 164727 715225 > 4²³³ [i]