MinT - Best Known (233−113, 233, s)-Nets in Base 4

Best Known (233−113, 233, s)-Nets in Base 4

(233−113, 233, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(233−113, 233, 181)-Net over F₄ — Digital

Digital (120, 233, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−113, 233, 2212)-Net in Base 4 — Upper bound on s

There is no (120, 233, 2213)-net in base 4, because

1 times m-reduction [i] would yield (120, 232, 2213)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 326170 522978 472101 568770 714137 395039 882237 979760 023132 036416 808109 161054 299718 335597 683830 502876 674040 964556 136840 357572 967865 017730 232400 > 4²³² [i]