MinT - Best Known (104, 104+47, s)-Nets in Base 4

Best Known (104, 104+47, s)-Nets in Base 4

(104, 104+47, 312)-Net over F₄ — Constructive and digital

Digital (104, 151, 312)-net over F₄, using

4¹ times duplication [i] based on digital (103, 150, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 50, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(104, 104+47, 566)-Net over F₄ — Digital

Digital (104, 151, 566)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+47, 26515)-Net in Base 4 — Upper bound on s

There is no (104, 151, 26516)-net in base 4, because

1 times m-reduction [i] would yield (104, 150, 26516)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 037070 964884 300503 081889 128357 544281 513363 141555 176576 232540 119817 719260 108132 155417 269536 > 4¹⁵⁰ [i]