MinT - Best Known (225−111, 225, s)-Nets in Base 4

Best Known (225−111, 225, s)-Nets in Base 4

(225−111, 225, 130)-Net over F₄ — Constructive and digital

Digital (114, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 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]

(225−111, 225, 166)-Net over F₄ — Digital

Digital (114, 225, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−111, 225, 1969)-Net in Base 4 — Upper bound on s

There is no (114, 225, 1970)-net in base 4, because

1 times m-reduction [i] would yield (114, 224, 1970)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 745 587926 720450 946545 095468 083128 489180 766636 479491 448186 715526 115060 294847 570991 056841 488069 351760 596773 115662 501837 316769 584947 227840 > 4²²⁴ [i]