MinT - Best Known (232−109, 232, s)-Nets in Base 4

Best Known (232−109, 232, s)-Nets in Base 4

(232−109, 232, 130)-Net over F₄ — Constructive and digital

Digital (123, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(232−109, 232, 199)-Net over F₄ — Digital

Digital (123, 232, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−109, 232, 2585)-Net in Base 4 — Upper bound on s

There is no (123, 232, 2586)-net in base 4, because

1 times m-reduction [i] would yield (123, 231, 2586)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 043534 025809 589000 849300 370415 931431 635065 549874 883626 238734 766931 075806 286999 645770 642277 324929 052418 306670 854168 306383 255912 202029 310400 > 4²³¹ [i]