MinT - Best Known (130, 233, s)-Nets in Base 4

Best Known (130, 233, s)-Nets in Base 4

(130, 233, 130)-Net over F₄ — Constructive and digital

Digital (130, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(130, 233, 242)-Net over F₄ — Digital

Digital (130, 233, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 233, 3584)-Net in Base 4 — Upper bound on s

There is no (130, 233, 3585)-net in base 4, because

1 times m-reduction [i] would yield (130, 232, 3585)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 679839 982749 573512 107931 300540 663281 031924 084712 070630 218019 729796 038929 459847 984066 788983 877874 938687 943981 223147 715040 903005 951887 352320 > 4²³² [i]