MinT - Best Known (203−81, 203, s)-Nets in Base 4

Best Known (203−81, 203, s)-Nets in Base 4

(203−81, 203, 130)-Net over F₄ — Constructive and digital

Digital (122, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(203−81, 203, 298)-Net over F₄ — Digital

Digital (122, 203, 298)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−81, 203, 5735)-Net in Base 4 — Upper bound on s

There is no (122, 203, 5736)-net in base 4, because

1 times m-reduction [i] would yield (122, 202, 5736)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 353256 740736 293003 123661 072885 596388 518088 460977 259877 424977 755286 145352 011327 667147 099445 915472 059449 289766 808688 807480 > 4²⁰² [i]