MinT - Best Known (229−45, 229, s)-Nets in Base 4

Best Known (229−45, 229, s)-Nets in Base 4

(229−45, 229, 1539)-Net over F₄ — Constructive and digital

Digital (184, 229, 1539)-net over F₄, using

5 times m-reduction [i] based on digital (184, 234, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(229−45, 229, 7842)-Net over F₄ — Digital

Digital (184, 229, 7842)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−45, 229, 5239153)-Net in Base 4 — Upper bound on s

There is no (184, 229, 5239154)-net in base 4, because

1 times m-reduction [i] would yield (184, 228, 5239154)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186071 195631 605116 211263 301253 021823 193592 319955 350397 328201 841735 237701 117144 513037 890301 522047 271046 486515 069978 265559 386809 700951 392240 > 4²²⁸ [i]